Question

In figure, $AP,AQ$ and $BC$ are tangents of the circle with centre $O$. If $AB=5cm,AC=6cm$ and $BC=4$ $cm$, then the length of $AP($ in $cm)$ is

• A. 9
• B. 15
• C. 10
• D. 7.5

Answer 1

The correct option is D 7.5

Due to tangents from external points, $BP=BR,CR=CQ$, and $AP=AQ$
Perimeter of $△ABC$,
$$\begin{array}{c}AB+BC+AC\\ =AB+BR+RC+AC\\ 5+4+6=AB+BP+CQ+AC\\ 15=AP+AQ\\ 15=2AP\end{array}$$
Thus $AP=\frac{15}{2}=7.5cm$