Question

In the figure, line l touches the circle with center O at point P. Q is the midpoint of radius OP. RS is a chord through Q such that chords RS || line l. If RS = 12 find the radius of the circle.

Answer 1

Let's say radius of the circle is $r$.

In the Given figure,

$OP=OR=Radius=r$

Since $OP\perp landl\parallel RS$

Hence,

Radius $OP\perp RS\left(chord\right)$

$RQ=QS=6unit$

As $Q$ is midpoint of $OP$

So, $OQ=\frac{r}{2}$

Using Pythagoras theorem in $△OQP$,

$O{R}^2=O{Q}^2+R{Q}^2$

$r^2=(\frac{r}{2}{)}^2+6^2$

$4r^2=r^2+144$

$3r^2=144$

$r^2=48orr\approx 7unit$

Hence, the radius of the circle is approx $7unit.$