ques.... AP, AQ and BC are tangents to the circle. If AB = 5CM , AC =6CM AND BC = 4CM, then find the length of AP .
Given: AQ, AP and BC are tangents to the circle with centre O and AB = 5cm , AC =6cm and BC = 4cm.
Let BS = x then CS = 4 – x
As, we know that tangents from an exterior point to a circle are equal in length
⇒AP=AQ
⇒ AB + BP = AC + CQ ........ (1)
BP = BS and CQ = CS .........(2)
from (1) and (2) we get
AB + BS = AC + CS
5+ x = 6 + (4– x)
⇒ x + x = 6+4-5
⇒ 2x = 5
⇒ x = 5/2=2.5
Hence, AP = AB + BP = AB + BS = 5 cm + 2.5 cm = 7.5cm