Question

The radii of two concentric circle are $13cm$ and $8cm$ and $AB$ is a diameter of the bigger circle. $BD$ is a tangent to the smaller circle touching it at $D$. Find the length $AD$. SOLUTION produce $BD$ to meet the bigger circle at $E$ Join $AE$ then.1561

Answer 1

Given $OA=OB=13cm$

$OD=8cm$

$\therefore AE=2\times OD=16cm$

$In△ODB$

$O{B}^2=O{D}^2+B{D}^2$

$B{D}^2=O{B}^2-O{D}^2$

$B{D}^2={13}^2-8^2$

$BD=\sqrt{105}cm$

$\therefore DE=BD=\sqrt{105}cm$

$In△ODB$

$A{D}^2=D{E}^2+A{E}^2$

$A{D}^2=(\sqrt{105}{)}^2+{16}^2$

$A{D}^2=105+256$

$AD=\sqrt{361}$

$AD=19cm$