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Standard IX

Mathematics

Theorem of Equal Chords Subtending Angles at the Center

In figure, A ...

Question

In figure, A, B, and C are three points on a circle with centre O such that $∠$ BOC = $30^{0}$ and $∠$ AOB = $60^{0}$ . If D is a point on the circle other than the arc ABC, find $∠$ ADC (in degrees).

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Solution

$∠$ ADC = $\frac{1}{2}$ $∠$ AOC (the angle subtended by an arc at the centre is double the angle subtended by it any point on the remaining part of the circle)

= $\frac{1}{2}$ [ $∠$ AOB + $∠$ BOC]

= $\frac{1}{2}$ [ $60^{\circ}$ + $30^{\circ}$ ]

= $45^{\circ}$

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Similar questions

In figure, A, B, and C are three points on a circle with centre O such that $∠$ BOC = $30^{0}$ and $∠$ AOB = $60^{0}$ . If D is a point on the circle other than the arc ABC, find $∠$ ADC (in degrees).

Q. In the given figure A, B and C are three points on a circle with centre O such that

∠ B O C = 30^{\circ}

and

∠ A O B = 60^{\circ}

. If D is a point on the circle other than the arc ABC, find

∠ A D C

in degrees.

Q. In figure

A, B

and

C

are three points on a circle with centre

O

such that

∠ B O C = 30^{o}

and

∠ A O B = 60^{o}

. If

D

is a point on the circle other than the arc

A B C

, find

∠ A D C

In the given figure, A, B and C are three points on a circle with centre O such that ∠BOC = 30° and ∠AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.

Q. In fig 10.36, A,B and C are three points on a circle with centre O such that

< B O C = 30^{0}

and

< A O B = 60^{0}

. If D is a point on the circle other that the are ABC, find <ADC.

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In figure, A, B, and C are three points on a circle with centre O such that ∠BOC = 300 and ∠AOB = 600. If D is a point on the circle other than the arc ABC, find ∠ADC (in degrees). __

∠ADC = 12∠AOC (the angle subtended by an arc at the centre is double the angle subtended by it any point on the remaining part of the circle) = 12 [∠AOB + ∠BOC] = 12 [60∘+ 30∘] = 45∘

In figure, A, B, and C are three points on a circle with centre O such that $∠$ BOC = $30^{0}$ and $∠$ AOB = $60^{0}$ . If D is a point on the circle other than the arc ABC, find $∠$ ADC (in degrees).

__

$∠$ ADC = $\frac{1}{2}$ $∠$ AOC (the angle subtended by an arc at the centre is double the angle subtended by it any point on the remaining part of the circle)

= $\frac{1}{2}$ [ $∠$ AOB + $∠$ BOC]

= $\frac{1}{2}$ [ $60^{\circ}$ + $30^{\circ}$ ]

= $45^{\circ}$