If AB, AC, PQ are tangents in the figure and $AB = 5\ cm$, find the perimeter of $\triangle APQ$.
"
Given:
AB, AC, PQ are tangents in the figure and $AB = 5\ cm$.
To do:
We have to find the perimeter of $\triangle APQ$.
Solution:
The lengths of the two tangents drawn from an external point to a circle are equal.
This implies,
PB and PX are tangents from P.
$PB = PX$
Similarly,
QC and QX are tangents from Q.
$QC = QX$
AB and AC are tangents from A.
$AB = AC$
Therefore,
Perimeter of $\triangle APQ= AP + PQ + AQ$
$= AP + PX + QX + AQ$
$= AP + PB + QC + AQ$ (since $PB = PX$ and $QC = QX$)
$= AB + AC$
$= AB + AB$ (since $AB=AC$)
$= 2 AB$
$= 2 \times 5$
$= 10\ cm$
The perimeter of $\triangle APQ$ is $10\ cm$.
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