In the given figure, O is the centre of the circle and BCD is tangent to it at C.

Question:

In the given figure, O is the centre of the circle and BCD is tangent to it at C. Prove that ∠BAC + ∠ACD = 90°.

Solution:

In the given figure, let us join D an A.

Consider . We have,

OC = OA (Radii of the same circle)

We know that angles opposite to equal sides of a triangle will be equal. Therefore,

 …… (1)

It is clear from the figure that

Now from (1)

Now as BD is tangent therefore 

Therefore 

From the figure we can see that 

Thus we have proved.

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