Check sibling questions

Example 2 - Two tangents TP and TQ are drawn from point T - Theorem 10.2: Equal tangents from external point (proof type)

Example 2 - Chapter 10 Class 10 Circles - Part 2
Example 2 - Chapter 10 Class 10 Circles - Part 3

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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 Given: A circle with centre O Two tangents TP and TQ to the circle where P and Q are the point of contact To prove: ∠ PTQ = 2 ∠OPQ Proof: We know from theorem 10.2 that length of tangents drawn from an external point to a circle are equal So, TP = TQ ∴ ∠ TQP = ∠ TPQ Now, PT is tangent, & OP is radius ∴ OP ⊥ TP So, ∠ OPT = 90° ∠ OPQ + ∠ TPQ = 90° ∠ TPQ = 90° – ∠ OPQ In Δ PTQ ∠ TPQ + ∠ TQP + ∠ PTQ = 180° ∠ TPQ + ∠ TPQ + ∠ PTQ = 180° 2∠ TPQ + ∠ PTQ = 180° 2(90° – ∠ OPQ)+ ∠ PTQ = 180° 2(90°) – 2∠ OPQ + ∠ PTQ = 180° 180° – 2∠ OPQ + ∠ PTQ = 180° ∠ PTQ = 180° – 180° + 2∠ OPQ ∠ PTQ = 2∠ OPQ Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.