100 Qs. 200 Marks 60 Mins
Diagram: Calculation: AB and AC are two equal chords of a circle, therefore the centre of the circle lies on the bisector of ∠BAC. ⇒ OA is the bisector of ∠BAC. Again, the internal bisector of an angle divides the opposite sides in the ratio of the sides containing the angle. P divides BC in the ratio = 6 : 6 = 1 : 1. ⇒ P is mid-point of BC. ⇒ OP ⊥ BC. In ΔABP, by Pythagoras theorem, AB2 = AP2 + BP2 ⇒ BP2 = 62 - AP2 ---- (1) In right triangle OBP, we have OB2 = OP2 + BP2 ⇒ 52 = (5 - AP)2 + BP2 ⇒ BP2 = 25 - (5 - AP)2 ---- (2) Equating (1) and (2), we get 62 - AP2 = 25 - (5 - AP)2 ⇒ 11 - AP2 = -25 - AP2 + 10AP ⇒ 36 = 10AP ⇒ AP = 3.6 cm Putting AP in (1), we get BP2 = 62 - (3.6)2 = 23.04 ⇒ BP = 4.8 cm ⇒ BC = 2BP = 2 × 4.8 = 9.6 cm = length of chord India’s #1 Learning Platform Start Complete Exam Preparation
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