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 ______.

Options

• 15 cm

• 10 cm

• 9 cm

• 7.5 cm

Answer 1

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 7.5 cm.

Explanation:

Let BP = x and CQ = y (B and C are vertices; the circle is tangent to BC at some point between B and C and to the extensions of AB, AC at P, Q).

From equal tangents from B and C we get BP = BT and CQ = CT,

So BC = BP + CQ 

⇒ x + y = 4

Also AP = AB + BP and AQ = AC + CQ and AP = AQ (tangents from A)

⇒ AB + x = AC + y 

⇒ x – y = AC – AB = 1

Solve x + y = 4 and x – y = 1

⇒ x = 2.5

Thus AP = AB + x

= 5 + 2.5

= 7.5 cm