I is the incentre of triangle PQR If ang PRQ 80 deg ang QIR 110 deg and QI 21 cm then what will be t...........

Quantitative Aptitude ( CCS) Geometry

I is the incentre of triangle PQR. If ∠PRQ = 80°, ∠QIR = 110° and QI = 21 cm, then what will be the area of the incircle?

376.5 cm²

346.5 cm²

364 cm²

396 cm²

छोटे Courses बड़े Results

Master Geometry

Prepare through Micro-courses

Try Now

Explanation:

Given that, I is the incentre of the triangle PQR and ∠PRQ = 80°
Now, ∠QIR = 110° and QI = 21 cm
Let ID ⊥ QR
∠QPR = 2(110 – 90) = 40°
(By the property of incircle)
∴ ∠PQR = 180 – ∠QPR – ∠PRQ
= 180 – 40 – 80 = 60°
∠IQD = ∠PQR /2 = 60/2 = 30°
Now, ID = IQ = sin30° =
20 x 1/2 = 21/2 cm
∴ Area of incircle = 22/7 x 21/2 x 21/2 = 346.5 cm²