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.
Explanation:
Let the radius of bigger circle (center X) be R cm.
Now, ∠QCY = ½ ∠BCA = 30°
∴ ∆CYQ is a 30°-60°-90° triangle
YQ = 2 ⇒ CY = 4 and CQ = 2√3
∆CXP is also a 30°-60°-90° triangle
∴ CX = 2 XP
⇒ (R + 2 + 4) = 2R
⇒ R = 6 cm
Hence, option (b).
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