Q. 155.0( 1 Vote )

A. 30 cm

B. 60 cm

C. 45 cm

D. 15 cm

Answer :

Given:

AQ = 4 cm

BR = 6 cm

PC = 5 cm

__Property:__*If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle) are equal.*

By the above property,

AR = AQ = 4 cm (tangent from A)

BR = BP = 6 cm (tangent from B)

CP = CQ = 5 cm (tangent from C)

Now,

Perimeter of ∆ABC = AB + BC + CA

⇒ Perimeter of ∆ABC = AR + RB + BP + PC + CQ + QA

[∵ AB = AR + RB

BC = BP + PC

CA = CQ + QA]

⇒ Perimeter of ∆ABC = 4 cm + 6 cm + 6 cm + 5 cm + 5 cm + 4 cm

⇒ Perimeter of ∆ABC = 30 cm

Hence, Perimeter of ∆ABC = 30 cm

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

RELATED QUESTIONS :

Which of the following statements is not true?

RS Aggarwal - MathematicsAssertion - and - Reason Type

Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

RS Aggarwal - Mathematics

Which of the following statements is true?

RS Aggarwal - MathematicsWhich of the following pairs of lines in a circle cannot be parallel?

RS Aggarwal - MathematicsThe chord of a circle of radius 10 cm subtends a right angle at its center. The length of the chord (in cm) is

RS Aggarwal - MathematicsIf a chord AB subtends an angle of 60° at the center of a circle, then the angle between the tangents to the circle drawn from A and B is

RS Aggarwal - MathematicsPQ is a tangent to a circle with center O at the point P. If ΔOPQ is an isosceles triangle, then ∠OQP is equal to

RS Aggarwal - MathematicsTo draw a pair of tangents to a circle, which is inclined to each other at an angle of 45°, we have to draw tangents at the end points of those two radii, the angle between which is

RS Aggarwal - MathematicsWhich of the following statements is not true?

RS Aggarwal - Mathematics