P and Q are centres of …
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Naveen Sharma 7 years, 1 month ago
Ans. If two circles touch each other externally, then sum of their radii is equal to the distance between their centres.
RP = x+9
RQ= x+2
PQ = 17
Given, angle PRQ= 90, So In Triangle PRQ => RP2 + RQ2 = PQ2 …(using Pythagoras)
=> (x+9)2 + (x+2)2= (17)2
=> x2 + 18x + 81 + x2 + 4x + 4 = 289
=> 2x2 + 22x -204 =0
=> x2 + 11x -102 = 0
On Solving We get
x = -17 and 6
So radius of circle is 6cm.
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