Question

In a circle with centre $O$, two unequal chords $PQ$ and $RS$ intersect each other at $M$, then $\Delta PMR$ and $\Delta QMS$ are

• A. congruent
• B. equal in area
• C. similar
• D. none of these

Answer 1

The correct option is C similar

For $△PMS$ and $△SMQ$
$1.\angle PMR=\angle QMS$ (Vertically opposite angle)
$2.\angle MPR=\angle MSQ$ (Angle subtended by the same arc are equal)
$3.\angle MRP=\angle MQS$ (Sum property of $△$).
Thus By $AAA$ criteria $△PMS$ $\approx$ $△SMQ$.
ANS- Option C