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In the figure given below $OA=5\ cm, AB=8\ cm$ and $OC$ is perpendicular to $AB$, then find the value of $CD$."

Given: In the figure $OA=5\ cm, AB=8\ cm$ and $OC$ is perpendicular to $AB$.


To do: To find the value of $CD$.


Solution:



As given $OA=5\ cm$

$AB=8\ cm$

$\because AB$ is a chord and $OC$ is perpendicular to $AB$.

Therefore $OC$ bisects $AB$.

$\Rightarrow AC=\frac{AB}{2}$

$\Rightarrow AC=\frac{8}{2}$

$\Rightarrow AC=4\ cm$

In right angled $\vartriangle OAC$,

$OA^2=OC^2+AC^2$                                 [Pythagoras theorem]

$\Rightarrow OC^2=OA^2-AC^2$

$\Rightarrow OC^2=5^2-4^2$

$\Rightarrow OC^2=25-16$

$\Rightarrow OC^2=9$

$\Rightarrow OC=\sqrt{9}$

$\Rightarrow OC=3\ cm$

We know that $CD=OD-OC$

$\Rightarrow CD=5-3$                          [$\because OD=OA=5\ cm=radius$]

$\Rightarrow CD=2\ cm$

Thus, $CD=2\ cm$

Updated on: 10-Oct-2022

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