Fig. 10.1.3Fig. 10.12XY and XY are two parallel tangents to a circle with centre 09. lo Fig 1013,another tangeer AB with point of contact C intersecting XY at A and XY aB

Fig. 10.1.3Fig. 10.12XY and XY are two parallel tangents to a circle w

1.	Fig. 10.1.3Fig. 10.12XY and XY are two parallel tangents to a circle with centre 09. lo Fig 1013,another tangeer AB with point of contact C intersecting XY at A and XY aB
Answer» I joined o and c In 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 º From equations (i) and (ii), 2∠COA + 2∠COB = 180º ⇒ ∠COA + ∠COB = 90º ⇒ ∠AOB = 90°