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In the given figure, *AB* and *CD* are diameters of a circle with centre *O*. If ∠*OBD* = 50°, find ∠*AOC*.

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#### Solution

It is given that, *AB* and *CD* are diameter with center *O* and `angleOBD = 50°`

We have to find `angle AOC`

Construction: Join the point *A* and *D* to form line *AD*

Clearly arc *AD* subtends`angle ABD = 50°` at *B* and `angleAOD` at the centre.

Therefore,

Since *CD* is a straight line then

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