The incircle of $Δ$ ABC touches the sides, AB, BC and AC in the point P, Q and R respectively. If AP $= 7$ cm, BC $= 13$ cm, find the perimeter of $Δ$ ABC.

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Solution

The correct option is C $40$ cm
In $△ A B C$
AB, BC and AC touches the circle at the point P, Q and R respectively.
$∴ B C + A P = A C + P B$
$⟹ 13 + 7 = A C + P B$
$⟹ A C = 20 - P B$
Perimeter of $△ A B C = A B + B C + A C$
$= A P + P B + 13 + 20 - P B$
$= 7 + 13 + 20 = 40$
$∴$ Perimeter of $△ A B C$ is $40$ cm.

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The incircle of ΔABC touches the sides, AB, BC and AC in the point P, Q and R respectively. If AP=7cm, BC=13cm, find the perimeter of ΔABC.

The correct option is C 40cmIn △ABCAB, BC and AC touches the circle at the point P, Q and R respectively.∴ BC+AP=AC+PB⟹ 13+7=AC+PB⟹ AC=20−PBPerimeter of △ABC=AB+BC+AC =AP+PB+13+20−PB =7+13+20=40∴ Perimeter of △ABC is 40 cm.

The incircle of $Δ$ ABC touches the sides, AB, BC and AC in the point P, Q and R respectively. If AP $= 7$ cm, BC $= 13$ cm, find the perimeter of $Δ$ ABC.