Question

In Figure 1,AP,AQ and BC are tangents to the circle. If AB=5 cm, AC= 6cm, and BC =4 cm,then the length of AP (in cm) is
A. 7.5
B. 15
C.10
D. 9

Answer 1

Answer:

Step-by-step explanation:

A. 7.5 cm

Construction - Draw line segment AD on triangle ABC.

We know, tangents drawn from an external point are equal.

Therefore,

AP = AQ

BP = BD

CQ = CD

Now,

Perimeter of the triangle ABC = 5 + 6 + 4 cm = 15 cm

AB + BC + AC = 15 cm

AB + BD + CD + AC = 15 cm (since BD + CD = BC)

AB + BP + CQ + AC = 15 cm

(AB + BP) + (CQ + AC) = 15 cm

AP + AQ = 15 cm

AP + AP = 15 cm

2AP = 15cm

AP = 15÷2 cm

AP = 7.5 cm