Question

Let C be a circle centre O. Let T be a point on the circle and P a point outside the circle such that PT is tangent to C. Assume that the segment OP intersects C in a point Q If PT = 12 and PQ = 8 the radius of C is

• A. $r=40$
• B. $r=5$
• C. $r=4\sqrt{5}$
• D. $r=4\sqrt{13}$

Answer 1

The correct option is B $r=5$

Let the radius of the circle be r. And PQ extended meets the other end of the circle at M
then, $P{T}^2=PQ\times PM$
${12}^2=8\times (8+2r)$
$18=8+2r$
$r=5$ cm