Number of Tangents from a Point | Tangent Theorem | Class 10 Circles | NCERT Examples | Faiz Sir

Welcome to Infinix Classes – Maths by Faiz Sir!
In today’s Class 10 Maths Chapter 10 Circles video, we discuss one of the most important topics:
⭐ Number of Tangents from a Point to a Circle
⭐ Tangent Theorem (Theorem 10.2)
⭐ Equal Lengths of Tangents from External Point
⭐ Complete Proof + NCERT Examples + Important Questions

🔵 आज के वीडियो में हम सीखेंगे:

✔ Theorem 10.2: External point se drawn tangents ki lengths equal hoti hain.
✔ Is theorem ka proof simple explanation ke saath.
✔ NCERT Example 1: Concentric circles & bisected chord explanation.
✔ NCERT Example 2: Prove that ∠PTQ = 2 ∠OPQ.
✔ NCERT Example 3: PQ = 8 cm, radius 5 cm → Find TP (full solution).
✔ Exam-based conceptual questions + tricks.

🔵 This video will help you with:

✔ Class 10 Board Exam
✔ NTSE / Olympiad Level Understanding
✔ NCERT + CBSE Sample Paper Preparation
✔ Strong conceptual clarity of tangents & circle geometry

⭐ Topics Covered:

Tangent to a Circle

External Point & Tangent Construction

Number of Tangents Possible

Equal Tangent Length Property

Proof using Geometry Concepts

NCERT Exercise Discussion

Important Diagrams + Explanation

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Number of Tangents from a Point on a Circle :
वृत्त पर एक बिंदु से स्पर्श रेखाओं की संख्या :


Theorem 10.2 : The lengths of tangents drawn from an external point to a circle are equal.
किसी बाह्य बिंदु से वृत्त पर खींची गई स्पर्श रेखाओं की लंबाइयाँ बराबर होती हैं।

Example 1 : Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.
सिद्ध कीजिए कि दो संकेन्द्रीय वृत्तों में, बड़े वृत्त की जीवा, जो छोटे वृत्त को स्पर्श करती है, संपर्क बिंदु पर समद्विभाजित होती है।



Example 2 : Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠ PTQ = 2 ∠ OPQ.
बाह्य बिंदु T से केंद्र O वाले वृत्त पर दो स्पर्श रेखाएँ TP और TQ खींची गई हैं। सिद्ध कीजिए कि ∠ PTQ = 2 ∠ OPQ है।

Example 3 : PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T (see Fig.). Find the length TP.
PQ, 5 सेमी त्रिज्या वाले एक वृत्त की 8 सेमी लंबाई वाली एक जीवा है। P और Q पर स्पर्श रेखाएँ एक बिंदु T पर प्रतिच्छेद करती हैं (चित्र देखें)। TP की लंबाई ज्ञात कीजिए।