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In the given figure, O is the centre of the given circle and m

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In the given figure, $O$ is the centre of the given circle and measure of arc $A BC$ is $10 0^{o}$ . Determine $∠ A D C$ and $∠ A BC$ .

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In the given figure,

O

is the centre of the given circle and measure of arc

A BC

10 0^{o}

. Determine

∠ A D C

and

∠ A BC

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

We know that the angle subtended by an arc is twice the angle subtended by it on the circumference

From the figure we know that

∠ A OC = 10 0^{o}

So we get

∠ A OC = 2∠ A D C

It can be written as

∠ A D C = \frac{1}{2} (10 0^{o})

So we get

∠ A D C = 5 0^{o}

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

It can be written as

∠ A D C + ∠ A BC = 18 0^{o}

By substituting the values

5 0^{o} + ∠ A BC = 18 0^{o}

On further calculation

∠ A BC = 18 0^{o} - 5 0^{o}

By subtraction

∠ A BC = 13 0^{o}

Therefore,

∠ A D C = 5 0^{o}

and

∠ A BC = 13 0^{o}

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Question Text	In the given figure, $O$ is the centre of the given circle and measure of arc $A BC$ is $10 0^{o}$ . Determine $∠ A D C$ and $∠ A BC$ .
Answer Type	Text solution:1
Upvotes	150

In the given figure, O is the centre of the given circle and measure of arc ABC is 100o. Determine ∠ADC and ∠ABC.

Text solutionVerified

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In the given figure, $O$ is the centre of the given circle and measure of arc $A BC$ is $10 0^{o}$ . Determine $∠ A D C$ and $∠ A BC$ .