Question

A chord of length $16cm$ is drawn in a circle of radius$10cm$. Find the distance of the chord from the center of the circle

Answer 1

Solve for the distance of the chord from the center of the circle

It is given that length of the chord $AB$$=16cm$ and radius of the circle $OA=10cm$
As we know perpendicular drawn from center of circle to chord bisect the chord .So $OC$ bisects the chord $AB$

$\therefore$Length of $AC=CB=8cm$

Use the Pythagoras theorem in $△OAC$

$$\begin{gathered} \Rightarrow O{A}^2=O{C}^2+A{C}^2 \\ \Rightarrow {10}^2=O{C}^2+8^2 \\ \Rightarrow 100=O{C}^2+64 \\ \Rightarrow O{C}^2=100-64 \\ \Rightarrow OC=6cm \end{gathered}$$
Hence the distance of the chord from the center of the circle is $6cm$