Changes
From Karnataka Open Educational Resources
18 bytes added
, 07:46, 14 August 2014
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| ==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{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 | + | ∠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 |