Question

3) Prove that : tangent segments drawn from an external point
to a circle are congruent.​

Answer 1

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Answer 2

Answer:

Given: A is the centre of the circle. Tangents through external point D touch the circle at the points P and Q. To prove: seg DP ≅ seg DQ Construction: Draw seg AP and seg AQ. Proof: In ∆PAD and ∆QAD, seg PA ≅ [segQA] [Radii of the same circle] seg AD ≅ seg AD [Common side] ∠APD = ∠AQD = 90° [Tangent theorem] ∴ ∆PAD = ∆QAD [By Hypotenuse side test] ∴ seg DP = seg DQ [c.s.c.t]Read more on Sarthaks.com - https://www.sarthaks.com/851335/theorem-tangent-segments-external-point-circle-congruent-radius-radius-complete-following