In a circle with centre O and radius 13 cm, a chord AB is drawn. Tangents at A and B intersect at P such that APB = 60º. If the distance of AB from the centre O is 5 cm, then what is the length (in cm) of AP?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 24.
Let PC = x cm.
In ACO,
OA2 = OC2 + AC2
AC2 = 132 - 52
AC2 = 144
AC = 12
Now in ACP,
Sin30° = AC/AP
1/2 = 12/AP
AP = 24 cm.