Question

In the figure AB is the diameter and CD is parallel to the diameter. AB = 8cm, BD = 2cm, find CD.

Answer 1

Drop $DP\perp AB$

So, $PA\times PB=P{D}^2$

$x(8-x)=P{D}^2\dots \left(1\right)$

In $\Delta PBD$

$P{D}^2=2^2-x^2\dots \left(2\right)$

from (1) & (2)

$x(8-x)=4-x^2$

$8x=4$

$x=\frac{1}{2}$

Similarly , draw $CQ\perp AB$

So, $AQ=\frac{1}{2}$

$PQ=8-(\frac{1}{2}+\frac{1}{2})=7cm$

So, CD=7 cm