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Learn Construction of tangents from external point

In CBSE Class 10 Mathematics, the "Constructions" chapter introduces students to precise geometric drafting. One of the most important and frequently tested concepts is the Construction of tangents from an external point to a given circle. A tangent is a straight line that touches the perimeter of a circle at exactly one point, known as the point of contact. Understanding how to accurately construct a pair of tangents from a point lying outside the circle is fundamental. It not only builds your spatial reasoning skills but also practically proves a key geometric theorem: exactly two tangents can be drawn to a circle from any external point, and the lengths of these two tangents are always equal.

The core logic behind this geometric construction relies on the foundational circle theorem that the angle in a semicircle is a right angle (90°). To construct the tangents, you must follow a series of logical steps: First, draw a circle with center O and a given radius, then mark the external point P. Join the points to create line segment OP. Next, construct the perpendicular bisector of OP to find its exact midpoint M. Using M as the new center and MO (or MP) as the radius, draw an auxiliary circle. The two points where this auxiliary circle intersects the original primary circle—let's name them A and B—are your exact points of contact. Finally, draw straight lines joining P to A, and P to B. Because the radii OA and OB are enclosed in the semicircles of the auxiliary circle, the angles ∠OAP and ∠OBP are strictly 90°. Since a line drawn perpendicular to a radius at the point of contact is a tangent, PA and PB are the required tangents.

Construction of Tangents from an External Point Step-by-step geometric construction to draw two equal length tangents (PA & PB) O P M A B Primary Circle Center O, Radius r Auxiliary Circle Center M, Radius MO Tangent PA PA ⊥ OA (Angle = 90°) Tangent PB Length PA = PB Perpendicular Bisector Locates Midpoint M

By studying the diagram above, you can clearly visualize this step-by-step construction process. The primary circle (highlighted in blue) and the external point P form the foundation of our problem. By bisecting the line OP with the green dashed line, we discover the exact center M needed to draft our auxiliary circle (shown as a dashed grey ring). The magical intersection happens exactly at points A and B. Because these points lie on the circumference of the auxiliary circle whose diameter is OP, the triangles created—ΔOAP and ΔOBP—are perfect right-angled triangles. In CBSE board exams, questions on this topic often ask students to perform this construction manually using a compass and ruler, and then mathematically verify that the measured lengths of PA and PB are identical. Mastering this visual logic ensures full marks in your geometry practicals.

Geometry can sometimes feel overwhelming with its intricate steps, precise measurements, and underlying theorems. If you are finding Class 10 Math challenging, connecting with an experienced tutor can make a world of difference. On UrbanPro, you can easily find highly qualified and verified CBSE Class 10 Mathematics tutors who specialize in breaking down complex topics into easy-to-understand concepts. Whether you prefer personalized one-on-one online tutoring or focused local offline tuition classes, UrbanPro is India's most trusted learning network. Find your perfect tutor today and boost your board exam preparation with confidence!


Other Concepts in Constructions


Other Concept Videos for Construction of tangents from external point

Drawing Tangents to a Circle from Outside video thumbnail

Drawing Tangents to a Circle from Outside

CBSE - Class 10>Mathematics>Constructions>Construction of tangents from external point


Drawing Tangents to a Circle from Outside video thumbnail

Drawing Tangents to a Circle from Outside

CBSE - Class 10>Mathematics>Constructions>Construction of tangents from external point

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Top Tutors who teach Construction of tangents from external point

Akshay Aggarwal Class 10 Tuition trainer in Delhi
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11 yrs of Exp 143 students
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Kapil Rai

I am utterly grateful to Akshay sir for his unending support and sincere guidance. He was such a big pillar of support in my board exams and his style of teaching is truly exceptional!!!! His notes, his previous year questions, his tips and his advices are really helpful for the board exams. I was able to score 97.2% in my boards because of his style of teaching. In fact all the topics he marked as important came in the board exams! Moreover he is a very hardworking and dedicated teacher with an unending passion to support and tutor children. I really am grateful to you Akshay sir Regards Nirvaan Rai Batch 2025-26

Skills: Mathematics , Physics and more
Also teaches: Class 6 Tuition, Class 8 Tuition and more

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With a decade of experience in teaching mathematics, physics, and chemistry for students from grades 8 through 12 across CBSE, IB, and ICSE boards, I offer a comprehensive educational approach that caters to a diverse range of curricula and learning needs. My academic background includes a BE and an MBA, equipping me with both technical and managerial skills that enhance my teaching methodology. Throughout my career, I have specialized in home tutoring, where I have developed a personalized approach to education that focuses on each student's unique needs and strengths. My sessions are designed to be interactive and engaging, fostering a learning environment where students feel supported and motivated. I conduct both online and offline classes, each lasting one hour, and utilize a variety of teaching tools to facilitate learning. I employ a whiteboard to visually explain concepts and provide question papers to help students practice and prepare for their exams. This hands-on approach ensures that students not only understand theoretical concepts but also develop problem-solving skills and confidence in their subjects. My commitment to delivering high-quality education and my extensive experience make me well-suited to guide students through their academic journey, helping them achieve their full potential in mathematics, physics, and chemistry.

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I have done b.Tech in electrical engineering from IIT KANPUR. I taught one year in akash institute patna, 2 years in fiitjee patna. Currently I am teaching in unacademy. I have taught more than 6000 jee and neet aspirants. In which more than 500 students are selected in iitand aiims. If some one is interested to improve their physics upto jee advanced level take help with me .And see the magic. I can help students in their all type of assignment from any institute like allen, fiitjee, narayna, akash, resonance. I can help students to solve both volume of h.C verma within two month if some one is intrested in solving I.E.Irodov join me and see the next level of physics. My way of teaching is so easy and so advanced that student will realyy enjoy it. Don't waste your time in making decision just join and experience my level

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He is a very dedicated teacher with excellent knowledge on topic. He knows Subject very well and teach accordingly to kids.

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Deepashree S. Class 10 Tuition trainer in Bangalore
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12 yrs of Exp 11 students
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With over 15 years of dedicated teaching experience, I am an accomplished and qualified educator specializing in Spoken English, Math, Science, Social Science, and Kannada Language. My expertise extends across various educational boards, including CBSE, ICSE, and state boards. Passionate about unraveling the mysteries of mathematical problems and chemical equations. I have garnered recognition with the prestigious Best Teacher Award for orchestrating state-level Science exams. Having contributed my skills to the esteemed MaxMuller Public School in Bangalore, I am committed to fostering a nurturing and inspiring learning environment. Join me on this educational journey where knowledge meets enthusiasm!

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Enrolled my 10-year-old for math tutoring, and the improvement is remarkable. The tutor identifies weak spots quickly, like multiplication tables. Fun drills with timers make practice competitive and enjoyable. She explains errors without blame, turning mistakes into lessons. Custom worksheets align with his CBSE curriculum spot-on. Confidence boost evident; he volunteers answers in class now. Test scores rose steadily over two months. Responsive to parent queries, even on weekends. Affordable rates for such quality one-on-one attention. Planning long-term enrollment—excellent choice!

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I've been teaching Class 10th students of schools from India and abroad. I primarily work with them to prepare for Olympiad, JEE foundation and school exams. I've been teaching students of class 8th-10th Science and Mathematics for more than 3 years. So far, I have taught more than 100 students from India and abroad. I teach international students Mathematics, Physics and Chemistry. I teach almost all boards of India such as CBSE, ICSE and state boards. I also teach IGCSE and IB students. I've my offline coaching institute where I am teaching students of CBSE and state boards who require help in Science and Mathematics. Fee displayed on my profile is for 1×1 classes. For group classes, the fee is substantially reduced.

Skills: Mathematics , Physics and more

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FAQ

What is the meaning of Construction of tangents from external point?

It refers to a specific mathematical method or property in Constructions used to solve problems involving Construction of tangents from external point.

Why is Construction of tangents from external point important for CBSE - Class 10 exams?

This concept is crucial for the exams as questions related to Constructions and specifically Construction of tangents from external point are very common. It helps secure marks in the section effectively.

Is Construction of tangents from external point part of the latest NCERT syllabus?

Yes, Construction of tangents from external point is an integral part of the CBSE - Class 10 NCERT Mathematics syllabus. It is a key topic covered in the Constructions chapter.

What are common mistakes students make with Construction of tangents from external point?

Students often miss the minute details or fundamental definitions of Construction of tangents from external point. Regular revision and practice are needed to master the nuances.

How should I approach learning Construction of tangents from external point?

Start by understanding the formulas and logic, then practice applying them to simple problems. Solve the examples given in the NCERT textbook before moving to exercise problems.

How can UrbanPro help me understand Construction of tangents from external point better?

UrbanPro connects you with experienced Mathematics tutors who can explain Construction of tangents from external point with simple examples. You also get access to doubt-clearing sessions and mock tests for better preparation.

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