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Circles Tangents Problems (view source)
Revision as of 07:42, 14 August 2014
, 07:42, 14 August 2014→Algorithm
==Algorithm==
==Algorithm==
In figure, AB is the diameter of circle C_{1} and AO is the diameter of the circle C_{2}<br>in △ADB and △ACO<br>
In figure, AB is the diameter of circle C_{1} and AO is the diameter of the circle C_{2}<br>in △ADB and △ACO<br>
∠ADB=90° and ∠ACO=90° [∵angles in the semi circles]<br>∠DAB=∠CAO [∵common angles]<br>△ADB∼△ACO [equiangular triangles are similar]<br><math>\frac{AB}{AO}</math>=<math>\frac{PD}{OC}</math>=<math>\frac{AD}{AC}</math> [corresonding sides of a similar triangles are proportional]<br>
∠ADB=90° and ∠ACO=90° [∵angles in the semi circles]<br>∠DAB=∠CAO [∵common angles]<br>△ADB∼△ACO [equiangular triangles are similar]<br><math>\frac{AB}{AO}</math>=<math>\frac{BD}{OC}</math>=<math>\frac{AD}{AC}</math> [corresonding sides of a similar triangles are proportional]<br>But AB=2OA----1 (diameter is twice the radius of a cicle)<br><math>\frac{AB}{AO}</math>=<math>\frac{BD}{OC}</math><br>from (1)<br><math>\frac{2OA}{AO}</math>=<math>\frac{BD}{OC}</math><br>BD=2OC