In the figure,OD is perpendicular to the chord AB of a side whose Centre is O. If BC is a diameter, show that C is equal to 2OD.
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Anonymous:
I think it should be BC, which is to prove 2OD. Please confirm...
I assume that you want me to prove that AC=2OD..
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Answer:
Step-by-step explanation:
In ∆ODB and ∆CAB
angle ODB=90°
angle CAB =90°(angle subtended by CB semicircle is 90°).
Angle CBA and Angle OBD are common angles.
By AA similarity criterion ∆ODB is similar to ∆CAB.
OD/AC=BO/BC
OD/AC=BO/2BO
OD/AC=1/2
2OD=AC.
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