Circle ' C prime has a diameter PQ and PS perpendicular to each other P X is any chord intersecting RS at Y, then PY. P X is equal to which one of the following?

Question

Circle ' C prime has a diameter PQ and PS perpendicular to each other P X is any chord intersecting RS at Y, then PY. P X is equal to which one of the following? (A) PC.CQ (B) PQ.PC (C) YC.XQ (D) PX.PC

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/b336b15fd6a8f49566284dae145407d8-.png" /> Join XQ. Since angle PXQ is inscribed on diameter So, angle PXQ =90° By Angle Angle similarity triangle PYC and triangle PQX are similar So (P Y/P C)=(P Q/P X) P Y ⋅ P X=P Q ⋅ P C

Q. Circle ' $C^{'}$ has a diameter $PQ$ and $PS$ perpendicular to each other $PX$ is any chord intersecting $RS$ at $Y$ , then $P Y$ . $PX$ is equal to which one of the following?

$PC . CQ$

$PQ . PC$

$Y C . XQ$

$PX . PC$

Join XQ.
Since angle PXQ is inscribed on diameter
So, $∠ PXQ = 9 0^{\circ}$
By Angle Angle similarity
$△ P Y C$ and $△ PQX$ are similar
So $\frac{P Y}{PC} = \frac{PQ}{PX}$
$P Y \cdot PX = PQ \cdot PC$

Q. Circle ' C′ has a diameter PQ and PS perpendicular to each other PX is any chord intersecting RS at Y, then PY. PX is equal to which one of the following?

PC.CQ

PQ.PC

YC.XQ

PX.PC