A circle is inscribed in a ^@ \triangle ABC ^@, touching ^@ BC, | Math Question and Answer

Answer:

$12 \space cm$

Step by Step Explanation:

We know that the lengths of tangents drawn from an external point to a circle are equal.
Thus, $\begin{aligned} & AR = AQ = 11 \space cm \\ & BP = BR \\ \text{ and } & CP = CQ = 9 \space cm \end{aligned}$
We see that $BR = AB - AR = 14 \space cm - 11 \space cm = 3 \space cm.$
Thus, $BP = BR = 3 \space cm.$
Therefore, $BC = BP + CP = 3 \space cm + 9 \space cm = 12 \space cm.$

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