Question

1. The figure shows two chords drawn on either sides of a diameter.
What is the length of the other chord?​

Answer 1

Step-by-step explanation:

PO is the perpendicular bisector of AB, OQ is the perpendicular bisector of AC.

∠OAQ = ∠OAP = 30° (Given)

∠OQA = ∠OPA = 90° (Right angles)

∴ ∠AOQ = ∠AOP (Third angle also equal)

AO = AO (Common side)

ΔOQA = ΔOPA

In equal triangles, sides opposite to equal angles are equal. So AP = AQ.

AP = ½AB (Perpendicular from the centre of a circle to a chord bisects the chord)

AQ = ½AC

Since AP = AQ

½AB = ½AC

AB = AC

So length of AC = 3 cm