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P and Q are centre of two circles with radii 9 cm and 2 cm respectively, where PQ = 17 cm. R is the centre of another circle of radius x cm, which touches each of the above two circles externally. If ∠PRQ = 90°, then the value of x is
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- 4 cm
- 6 cm
- 7 cm
- 8 cm
- 4 cm
Correct Option: B
According to question , we draw a figure of two circles with radii 9 cm and 2 cm and R is the centre of another circle of radius x cm 
Given , ∠PRQ = 90°
From figure , PR = 2 + x
PQ = 17
RQ = 9 + x
From ∆PRQ ,
∴ PQ² = PR² + RQ²
⇒ 17² = (2 + x)² + (9 + x)²
⇒ 289 = 4 + 4x + x² + 81 + 18x + x²
⇒ 289 = 2x² + 22x + 85
⇒ 2x² + 22x + 85 – 289 = 0
⇒ 2x² + 22x – 204 = 0
⇒ x² + 11x – 102 = 0
⇒ x² + 17x – 6x – 102 = 0
⇒ x(x + 17) – 6 (x + 17) = 0
⇒ (x – 6) (x + 17) = 0
⇒ x = 6 as x ≠ –17
∴ x = 6 cm
