A circles is inscribed in a $△ A B C$ touching $A B, B C$ and $A C$ at $P, Q$ and $R$ respectively. If $A B = 10 c m, A R = 7 c m$ and $C R = 5 c m$ ., find the length of $B C$

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Solution

Given, a circle inscribed in $△ A B C$ , such that the circle touches the sides of the triangle.
Tangents drawn to a circle from an external point are equal.
$∴ A P = A R = 7$ cm
$C Q = C R = 5$ cm
Now, $B P = A B - A P = 10 - 7 = 3$ cm
$∴ B P = B Q = 3$ cm
$∴ B C = B Q + Q C = 3 + 5 = 8$ cm
$∴$ the length of $B C$ is $8$ cm

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A circles is inscribed in a △ABC touching AB,BC and AC at P,Q and R respectively. If AB=10cm,AR=7 cm and CR=5cm., find the length of BC

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