In the given figure, ABC is a right angled triangle. ∠ABC = 90° and ∠ACB = 60°. If the radius of the smaller circle is 2 cm, then what is the radius (in cm) of the larger circle ?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 6.
∠ACB = 60°, ∠ACP = ∠PCB = 30°.
In triangle CPD;
Sin30 = PD/CP
∴ CP = 4 cm
In triangle CQE;
Sin30 = QE/CQ
QC = 2QE
Let radius of larger circle = QE = QO = R cm
∴ QC = 2R
QC = QO + OP + PC
⇒ 2R = R + 2 + 4
⇒ R = 6 cm
∴ Radius of larger circle = 6 cm