Question

The radii of two concentric circles are $13cm$ and $8cm$. $AB$ is a diameter of the bigger circle and $BD$ is a tangent to the smaller circle touching it at $D$ and intersecting the larger circle at $P$ on producing. Find the length of $AP$.

Answer 1

R = 13 CM

angle ODB $={90}^{\circ }$ (BD is tangent)

angle APB $={90}^{\circ }$ (angle in semicircle)

angle DBO = angle PBA (common)

So, By AA criteria tri APB similar to tri DBO

By $CPST..BD/BP=BO/AB=OD/AP$

$OD/AP=BO/AB$

$S/AP=13/26$

$AP=16cm$