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In the adjoining figure, DE is a chord parallel to a diameter

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In the adjoining figure, $D E$ is a chord parallel to a diameter $A C$ of the circle with centre $O$ . If $∠ CB D = 6 0^{o}$ , calculate $∠ C D E$ .

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Oliver Discussed

In the adjoining figure,

D E

is a chord parallel to a diameter

A C

of the circle with centre

O

. If

∠ CB D = 6 0^{o}

, calculate

∠ C D E

12 mins ago

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Text solutionVerified

We know that the angles in the same segment of a circle are equal

From the figure we know that

∠ C A D

and

∠ CB D

are in the segment

C D

∠ C A D = ∠ CB D = 6 0^{o}

An angle in a semi-circle is a right angle

So we get

∠ A D C = 9 0^{o}

Using the angle sum property

∠ A C D + ∠ A D C + ∠ C A D = 18 0^{o}

By substituting the values

∠ A C D + 9 0^{o} + 6 0^{o} = 18 0^{o}

On further calculation

∠ A C D = 18 0^{o} - 9 0^{o} - 6 0^{o}

By subtraction

A C D = 18 0^{o} - 15 0^{o}

So we get

∠ A C D = 3 0^{o}

We know that

A C ∣∣ D E

and

C D

is a transversal

From the figure we know that

∠ A C D

and

∠ C D E

are alternate angles

So we get

∠ C D E = ∠ A C D = 3 0^{o}

Therefore,

∠ C D E = 3 0^{o}

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Question Text	In the adjoining figure, $D E$ is a chord parallel to a diameter $A C$ of the circle with centre $O$ . If $∠ CB D = 6 0^{o}$ , calculate $∠ C D E$ .
Answer Type	Text solution:1
Upvotes	150

In the adjoining figure, DE is a chord parallel to a diameter AC of the circle with centre O. If ∠CBD=60o, calculate ∠CDE.

Text solutionVerified

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In the adjoining figure, $D E$ is a chord parallel to a diameter $A C$ of the circle with centre $O$ . If $∠ CB D = 6 0^{o}$ , calculate $∠ C D E$ .