In the figure,two chords $AB$ and $CD$ intersect each other at the point $P$. Prove that $\Delta APC \sim \Delta DPB$.
(N/A) To prove that $\Delta APC \sim \Delta DPB$,we follow these steps:
$1$. Join $CB$ and $AD$.
$2$. Consider $\Delta APC$ and $\Delta DPB$.
$3$. $\angle APC = \angle DPB$ (Vertically opposite angles).
$4$. $\angle CAP = \angle BDP$ (Angles subtended by the same arc $CB$ in the same segment of the circle are equal).
$5$. Therefore,by the $AA$ (Angle-Angle) similarity criterion,$\Delta APC \sim \Delta DPB$.
$1$. Join $CB$ and $AD$.
$2$. Consider $\Delta APC$ and $\Delta DPB$.
$3$. $\angle APC = \angle DPB$ (Vertically opposite angles).
$4$. $\angle CAP = \angle BDP$ (Angles subtended by the same arc $CB$ in the same segment of the circle are equal).
$5$. Therefore,by the $AA$ (Angle-Angle) similarity criterion,$\Delta APC \sim \Delta DPB$.
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