P is a point outside a circle and is 26 cm away from its centre. A secant PAB drawn from intersects the circle at points A and B such that PB = 32 cm and PA= 18 cm. The radius of the circle (in cm)is:
Answer & explanation
Correct answer: option 3
Let PQ = (26 + r)
and PT = (26 - r)
As we know,
= PT x PQ = PA x PB
= (26 + r) x (26 - r) = 18 x 32
= \( {26 }^{2 } \) - \( {r }^{2 } \) = 576
= \( {r }^{2 } \) = 676 - 576
= \( {r }^{2 } \) = 100
= r = \(\sqrt {100 }\) = 10 cm.