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Theorem 10.8 : The angle subtended by an...

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.

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To prove Theorem 10.8: "The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle," we can follow these steps: ### Step-by-Step Solution: 1. **Draw the Circle and Identify Points**: - Draw a circle with center \( O \). - Let \( P \) and \( Q \) be two points on the circumference of the circle, creating an arc \( PQ \). - Choose any point \( A \) on the remaining part of the circle. ...
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x-y+b=0 is a chord of the circle x^2 + y^2 = a^2 subtending an angle 60^0 in the major segment of the circle. Statement 1 : b/a = +- sqrt(2) . Statement 2 : The angle subtended by a chord of a circle at the centre is twice the angle subtended by it at any point on the circumference. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

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Knowledge Check

  • The angle subtended by an arc of length 20 cm at the centre of circle when radius is 14 cm is

    A
    `5/(7)` radians
    B
    `10/(7)` radians
    C
    `5/(14)` radians
    D
    `7/(10)` radians

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