Question

a secant of a circle intersects the circle at point A and B. A tangent PT intersects the secant a point in the exterior of the circle and touches the circle at T. If PT =
$5 \sqrt{2}$
and AP = 5. Find PB​

Answer 1

Answer:

If a secant and a tangent of a circle intersect in a point outside the circle, then the area of the rectangle formed by the two line segments corresponding to the secant is equal to the area of the area of the square formed by the line segment corresponding to the other tangent.

Explanation:

Given that,

PT is a tangent and PAB is a secent.

To prove that,

PT

2

=

PA×

PB

Construction : Draw seg BT and AT

In ΔPAT and ΔPBT

∠PTA= ∠PBT

∠TPA= ∠TPB

∴ ΔPAT∼ ΔPBT

P B

P T

=

P T

P A

PT

2

= PA× PB

Hence, proved in image