Question

In a ΔPJK, PJ = JK = PK. The ratio of the radius of the circumcircle to that of the incircle is

1. 2 : 1
2. 3 : 2
3. 1 : 4
4. 4 : 1

Answer 1

Correct Answer - Option 1 : 2 : 1

Given:

ΔPJK, PJ = JK = PK

Formula used:

Radius of incircle (r) = (Side/2√3)

Radius of circumcircle (R) = (Side/√3)

Calculation:

In ΔPJK,

PJ = JK = PK

Hence, ΔPJK is an equilateral triangle.

Let r be the radius of incircle and R be the radius of circumcircle.

Radius of incircle (r) = (PJ/2√3)

Radius of circumcircle (R) = (PJ/√3)

So, the required ratio

⇒ R ∶ r = (PJ/√3) ∶ (PJ /2√3)

⇒ R ∶ r = 2 ∶ 1

∴ The required answer is 2 ∶ 1.