**Question:**

In the given figure, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm then the length of AP is

(a) 15 cm

(b) 10 cm

(c) 9 cm

(d) 7.5 cm

**Solution:**

We know that tangent segments to a circle from the same external point are congruent.

Therefore, we have

AP = AQ

BP = BD

CQ = CD

Now, AB + BC + AC = 5 + 4 + 6 = 15

⇒AB + BD + DC + AC = 15 cm

⇒AB + BP + CQ + AC = 15 cm

⇒AP + AQ= 15 cm

⇒2AP = 15 cm

⇒AP = 7.5 cm

Hence, the correct answer is option(d)