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The angle subtended by an arc of a circl...

The angle subtended by an arc of a circle at the centre is double the angle subtended by it any point on the remaining part of the circle.

Text Solution

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The correct Answer is:
`/_ACD=54^(@)`
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Theorem 10.8 : The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Consider the following statements 1. the opposite angles of a cyclic quadrilateral are supplementary. 2. Angle subtended by an arc at the centre is doubled the angle subtended by it any point on the remaining part of the circle. Which one of the following is correct in respect of the above statements

Knowledge Check

  • The total plane angle subtended by a circle at its centre is

    A
    `pi` rad
    B
    `2pi` rad
    C
    `(2pi)/3` rad
    D
    `pi/2` rad

  • If the chord of a circle is equal to the radius of the circle,then the angle subtended by the chord at a point on the minor arc is:

    A
    `120^@`
    B
    `150^@`
    C
    `100^@`
    D
    `110^@`

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    Show that any angle in a semi-circle is a right angle. The following arc the steps involved in showing the above result. Arrange them in sequential order. A) therefore angleACB=180^(@)/2=90^(@) B) The angle subtended by an arc at the center is double of the angle subtended by the same arc at any point on the remaining part of the circle. c) Let AB be a diameter of a circle with center D and C be any point on the circle. Join AC and BC. D) therefore angleAD = 2 xx angleACB 180^(@)=2angleACB(therefore angleADB=180^(@))

    Theorem:-5(i) The degree measure of an arc or angle subtended by an arc at the centre is double the angle subtended by it at any point of alternate segment.(ii) Angle in the same segment of a circle are equal (iii) The angle in the semi circle is right angle.

    Angle subtend by an arc at center is double the angle subtend b it at any point on remaining part OF circle||Angle is a semi circle is a 90 ||Example ||Congurent arc|| Equal arc||Cyclic quadrilateral

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    The length of a minor arc is 2/9 of the circumference of the circle. Write the measure of the angle (in degrees) subtended by the arc at the centre of the circle.

    Given an are PQ of a circle subtending angles POQ at the centre PAQ at a point A on the remaining part of the circle.We need to prove that /_POQ=2/_PAQ.

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