In the given figure OD is perpendicular to the chord AB of a circle whose centre is o . if BC is a diameter , show that CA = 2OD....
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Step-by-step explanation:
In ΔBOD and ΔBCA
∠ODB = ∠CAB ( each of 90°)
∠OBD = ∠CBA ( common angles are equal to each other)
So, by AA postulate of similarity of triangles, ΔBOD ~ ΔBCA
Now, sides of similar triangles are proportional to each other.
==> CA/OD = BC/BO
==> CA/OD = 2BO/BO
==> CA = 2OD
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