Question

In fig, point $A$ is a centre of a circle $AP=34$, $A$ is the centre of the circle, $AM=30$. If seg $AM$, $\perp$ seg $PQ$, find the length of chord $PQ$,

• A. $32$ cm
• B. $64$ cm
• C. $8$ cm
• D. $16$ cm

Answer 1

The correct option is A $32$ cm

Given- $AP=34$ cm is the radius of a circle with centre $A$.

$AM=30$ cm and $AM\perp PQ$

To find out- The length of P$Q=?$

Solution-

$\Delta AMP$ is a right one with $AP$ as hypotenuse, since $AM\perp PQ$ at $M$.

So, by Pythagoras theorem, we have

$PM=\sqrt{{AP}^2-{PM}^2}=\sqrt{{34}^2-{30}^2}=16$ cm.

So, $QM=PM=16$ cm

$\Rightarrow QM+PM=PQ=16$cm $+16$ cm $=32$cm.