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. P & Q are centres of circles of radii 9 cm and 2cm respectively, PQ = 17 cm, R is the centre ofthe circle of radius x cm which touches the aboveexternally. Given that angle PRO is 90°. Write anequation in x and solve it |
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Answer» Clearly,PQ= 17PR=x+9RQ= x+2So, from pythagoras theorem,PR² + RQ² = PQ²(x+9)² + (x+2)² = 17²Which gives 2x² + 22x + 85 = 289which gives x² + 11x - 102= 0as the required equation.solving, we get , x=6 or -17 Since radius cannot be negative, so x= 6 |
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