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Question

In the given figure, O is the centre of circle and DAB=50o. Calculate the values of x and y.
1715725_43e290f87a2849c99ba340f999fce990.png

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Solution

It is given that O is the centre of the circle and DAB=50o

We know that the radii of the circle are equal

OA=OB

From the figure we know that

OAB+OBA+AOB=180o

By substituting the values

50o+50o+AOB=180o

On further calculation

AOB=180o50o50o

By subtraction

AOB=180o100o

So we get

AOB=80o

From the figure we know that AOD is a straight line

It can be written as

x=180oAOB

By substituting the values

x=180o80o

By subtraction

x=100o

We know that the opposite angles of a cyclic quadrilateral are supplementary

So we get

DAB+BCD=180o

By substituting the values

50o+BCD=180o

On further calculation

BCD=180o50o

By subtraction

y=BCD=130o

Therefore the value of x is 100o and y is 130o.

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