Question

in the figure AQ, AR and BC are tangents to a circle with centre O. if AB=7cm ,BC= 5cm, AC=5cm then length of the tangents AQ is

Answer 1

Since all the sides of the triangle are not unequal we can say that the triangle is a scalene triangle....

Answer 2

Explanation:

AQ, AR and BC are tangents to a circle with centre O

AB=7cm ,BC= 5cm, AC=5cm

If you consider BS = X and CS = 5X. The tangent that is drawn from the exterior of the circle would be equal and the length of the tangents AQ would be equal to AR Answer - 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