A secant is drawn from a point P to a circle so that it meets the circle first at A, then goes through the centre, and leaves the circle at B. If the length of the tangent from P to the circle is 12 cm, and the radius of the circle is 5 cm, then the distance from P to A is:

A. 8 cm

B. 12 cm

C. 18 cm

D. 10 cm

Answer: Option A

Solution (By Examveda Team)

PQ = 12 cm
r = 5 cm
PQ² = PA × PB
12² = x(x + 10)
144 = x(x + 10)
x² + 10x - 144 = 0
x² + (18x - 8x) -144 = 0
x(x + 18) - 8(x + 18) = 0
x = 8, x = -18
PA = 8 cm