Changes

In figure, AB is the diameter of circle <math>C_{1}</math> and AO is the  diameter of the circle <math>C_{2}</math><br>in △ADB and △ACO<br>

In figure, AB is the diameter of circle <math>C_{1}</math> and AO is the  diameter of the circle <math>C_{2}</math><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}{OA}</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}{OA}</math>=<math>\frac{BD}{OC}</math><br>from (1)<br><math>\frac{2OA}{OA}</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}{OA}</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}{OA}</math>=<math>\frac{BD}{OC}</math><br>from (1)<br><math>\frac{2OA}{OA}</math>=<math>\frac{BD}{OC}</math><br>∴BD=2OC