If PA and PB are tangents from an outside point P. Such that PA = 10cm and ∠APB = 60°. Find the length of cord AB.
Given : PA and PB are tangents of a circle, PA = 10 cm and ∠APB = 60°
Let O be the center of the given circle and C be the point of intersection of OP and AB
In ΔPAC and ΔPBC
PA = PB ( Tangents from an external point are equal)
∠APC = ∠BPC ( Tangents from an external point are equally inclined to the segment joining center to that point)
PC = PC ( Common)
Thus ΔPAC ΔPBC (By SAS congruency rule) ..........(1)
∴ AC = BC
Also ∠APB = ∠APC + ∠BPC
∠ACP + ∠BCP = 180°
Now in right triangle ACP
∴ AB = AC + BC = AC + AC ( AC = BC)
⇒ AB = (5 + 5) cm = 10 cm