Question

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

Answer 1

Correct option is A. $$7.5$$
Since we know that length of tangents drawn on cine from an external point are equal
So, $$BP = BD$$ (Tangents on circle from point $$B$$) .....(i)
$$CQ = CD$$ (Tangents on circle from point $$C$$) .....(ii)
$$AP = AQ$$ (Tangents on circle from point $$A$$) .....(iii)
$$AP = AB + BP \Rightarrow AP =AB + BD$$ .....(iv)
$$AQ = AC + CQ \Rightarrow AQ = AC + CD$$ .....(v)
Adding equation (iv) and (v)
$$ AP + AQ = AB + BD + AC + CD$$
$$\Rightarrow AP + AP = AB + BC + AC$$ [By using equation (iii)]
$$\Rightarrow 2 AP = 11 + BC$$
$$\Rightarrow 2 AP = 11 + 4$$
$$\Rightarrow 2 AP = 15 \Rightarrow AP = 7.5 cm$$
Hence, correct choice is (A).