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In the given figure, $\Delta ABC$ circumscribes a circle. If $AR = 3 \text{ cm}$, $BP = 4 \text{ cm}$ and $QC = 5 \text{ cm}$, find the perimeter of $\Delta ABC$.
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Solution: As the length of tangents from an external point to a circle are equal
$BP = BR = 4 \text{ cm}$
$CQ = CP = 5 \text{ cm}$
$AR = AQ = 3 \text{ cm}$ [1 mark]
Perimeter of $\Delta ABC = AB + BC + AC$
$= 7 + 9 + 8$ [1/2 mark]
$= 24 \text{ cm}$ [1/2 mark]
$BP = BR = 4 \text{ cm}$
$CQ = CP = 5 \text{ cm}$
$AR = AQ = 3 \text{ cm}$ [1 mark]
Perimeter of $\Delta ABC = AB + BC + AC$
$= 7 + 9 + 8$ [1/2 mark]
$= 24 \text{ cm}$ [1/2 mark]