A PFig. 10.13Fig, 1n.12another tangent AB with point of contact C intersecting XY at Athat < AOB = 90Â°.9. In Fig. 10.13, XY and X'Y' are two parallel tangents to a circle wlatuieen the (wo tangents drawn from an externalpoint to a

A PFig. 10.13Fig, 1n.12another tangent AB with point of contact C inte

1.	A PFig. 10.13Fig, 1n.12another tangent AB with point of contact C intersecting XY at Athat < AOB = 90Â°.9. In Fig. 10.13, XY and X'Y' are two parallel tangents to a circle wlatuieen the (wo tangents drawn from an externalpoint to a
Answer» I joined o and cIn ΔOPA and ΔOCA, OP = OC (Radii of the same circle) AP = AC (Tangents from point A) AO = AO (Common side)∴ ΔOPA ≅ ΔOCA (SSS congruence criterion)⇒ ∠POA = ∠COA … (i)Similarly, ΔOQB ≅ ΔOCB ∠QOB = ∠COB … (ii)Since POQ is a diameter of the circle, it is a straight line.∴ ∠POA + ∠COA + ∠COB + ∠QOB = 180 ºFrom equations (i) and (ii),2∠COA + 2∠COB = 180º⇒ ∠COA + ∠COB = 90º⇒ ∠AOB = 90°