Question

In Figure 1, 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 (in cm) is

विकल्प

• A. 7.5

• B. 15

• C. 10

• D. 9

Answer 1

AP, AQ and BC are tangents to the circle. Suppose BC touch the circle at R.

It is given that AB = 5 cm, AC = 6 cm and BC = 4 cm.

We know that, the lengths of tangents drawn from an external point to a circle are equal.

∴ AP = AQ … (1)

PB = BR … (2)

CQ = CR .... (3)

2AP = AP + AP

∴ 2AP = AP + AQ [Using (1)]

⇒ 2AP = (AB + PB) + (AC + CQ)

⇒ 2AP = (AB + BR) + (AC + CR) [Using (2) and (3)]

⇒ 2AP = AB + (BR + CR) + AC

⇒ 2AP = AB + BC + AC

⇒ 2AP = 5 cm + 4 cm + 6 cm

⇒ 2AP = 15 cm

⇒ AP = 7.5 cm

Thus, the length of AP is 7.5 cm.

Hence, the correct answer is A.