Question

$O$ is the centre of a circle with radius $5$ cm. $LM$ is the diameter of the circle. $P$ is a point on the plane of the circle such that $LP=6$ cm and $MP=8$ cm. Then $P$ lies.

• A. on $LM$
• B. outside the circle
• C. inside the circle
• D. on the circle.

Answer 1

Answer: (D)

on the circle.

Let O be the center of the circle. LM is the diameter,
$LM=2\times OL=(2\times 5)$ cm$=10$ cm
$L{P}^2+P{M}^2=6^2+8^2=36+64=100$
and $L{M}^2={10}^2=100$
$\Rightarrow$ $L{P}^2+P{M}^2=L{M}^2\Rightarrow △LPM$ is right angled triangle, rt. $\angle d$ at $P\Rightarrow \angle LPM={90}^{\circ }$
$\Rightarrow$ $P$ lies on the circumference of the circle (Since, Angle in a semi-circle is a rt. $\angle$)