Ex 10.2, 4 - Prove that tangents drawn at ends of a diameter - Theorem 10.1: Tangent perpendicular to radius (proof type)

Ex 10.2, 4 - Chapter 10 Class 10 Circles - Part 2

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Ex 10.2,4 Prove that the tangents drawn at the ends of a diameter of a circle are parallel. Given: A circle with center O And diameter AB Let PQ be the tangent at point A & RS be the tangent at point B To prove: PQ ∥ RS Proof: Since PQ is a tangent at point A OA ⊥ PQ ∠ OAP = 90° Similarly, RS is a tangent at point B OB ⊥ RS ∠ OBS = 90° From (1) & (2) ∠ OAP = 90° & ∠ OBS = 90° Therefore ∠ OAP = ∠ OBS i.e. ∠ BAP = ∠ ABS For lines PQ & RS, and transversal AB ∠ BAP = ∠ ABS i.e. both alternate angles are equal So, lines are parallel ∴ PQ II RS

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo