Mathematics
In the adjoining figure, sides BC, CA and AB of △ABC touch a circle at the points P, Q and R respectively. If PC = 5 cm, AR = 4 cm and RB = 6 cm, then the perimeter of △ABC is
60 cm
45 cm
30 cm
15 cm
Answer
We know that if two tangents are drawn from an external point to a circle then, the lengths of the tangents are equal.
∴ BP = BR = 6 cm, CQ = CP = 5 cm and AQ = AR = 4 cm.
Perimeter of △ABC ⇒ AB + BC + CA
⇒ AR + BR + BP + CP + AQ + CQ
⇒ 4 + 6 + 6 + 5 + 4 + 5
⇒ 30 cm.
Hence, Option 3 is the correct option.
Related Questions
In the adjoining figure, sides BC, CA and AB of △ABC touch a circle at point D, E and F respectively. If BD = 4 cm, DC = 3 cm and CA = 8 cm, then the length of side AB is
12 cm
11 cm
10 cm
9 cm
PQ is a tangent to a circle at point P. Centre of circle is O. If △OPQ is an isosceles triangle, then ∠QOP is equal to
30°
60°
45°
90°
In the adjoining figure, PA and PB are tangents to a circle with centre O. If ∠APB = 50°, then ∠OAB is equal to
25°
30°
40°
50°
In the adjoining figure, PA and PB are tangents at points A and B respectively to a circle with centre O. If C is a point on the circle and ∠APB = 40°, then ∠ACB is equal to
80°
70°
90°
140°
