Question

In the following figure, AP, AQ and BC are tangents of the circle with centre O. If AB = 5 cm, AC = 6 cm and BC = 4 cm, then the length of AP (in cm) is

विकल्प

• 15

• 10

• 9

• 7.5

Answer 1

7.5

Explanation:

Perimeter of ΔABC = AB + BC + AC

= AB + BR + RC + AC

= (AB + BP) + (CQ + AC)   ...[∵ BD = BQ, CD = CQ, (tangents from external points)]

= AP + AQ

= 2AP   ...[∵ AP = AQ, tangents from external point]

∴ AB + BC + AC = 2AP

⇒ 5 + 4 + 6 = 2AP

⇒ AP = `15/2`

⇒ AP = 7.5 cm