P is a point outside a circle with centre O, and it is 14 cm away from the centre. A secant PAB drawn from P intersects the circle at the points A and B such that PA = 10 cm and PB = 16 cm. The diameter of the Circle is:
Answer & explanation
Correct answer: option 3
Given OP = 14 cm, PA = 10 cm, PB = 16 cm
Let radius of circle be r cm.
= OQ = OE = r cm
= PR = (14 - r) and PQ = (14 + r)
As we know,
PE x PQ = PA x PB
= (14 - r)(14 + r)= 10 x 16
= \( { 14}^{2 } \) - \( { r}^{2 } \) = 160
= 196 - \( { r}^{2 } \) = 160
= \( { r}^{2 } \) = 196 - 160 = 36
= r = \(\sqrt {36 }\) = 6 cm
Therefore, Diameter 2 x 6 = 12 cm.