Geometric Tangential Circles

Geometry Level 2

Hint: Look for similar triangles.


The answer is 91.

HariShankar Pv by HariShankar PV , 21, India

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1 solution

HariShankar Pv
Mar 26, 2014

From similar triangles ABM and BCL , we have CL/BM = CB/BA

= r1 - r / r1 + r = r - r2 / r + r2

= r1 / r = r / r2

= r square = r1 * r2

Given that r1 = 13 and r2 = 7 , then r square = 13 * 7 = 91

10 Helpful 0 Interesting 0 Brilliant 0 Confused

r2=91

Chandrakant Tupsoundarya - 7 years, 2 months ago

r^2=91

Hargovind Singh - 7 years, 2 months ago

91

Mahmudul Hasan Jewel - 7 years, 2 months ago

(r1-r)/(r1+r)= (r-r2)/(r+r2); (13-r)/(13+r)=(r-7)/(r+7) (13-r) (r+7)=(13+r) (r-7) Solves to yield r squared = 91

Anderson Schroeder - 7 years, 2 months ago

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