Angle Subtended by an Arc of a Circle#!#Part 2

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.

Theorem 2: The no.of Radians in an angle subtended by an arc of a circle at the centre = arc/radius

The radius of a circle is 14cms. The angle subtended by an arc of the circle at the centre is 45^(@) . Find the length of the arc.

Revision|Questions|Angle Subtended By An Arc Of A Circle|Theorem|Cyclic Quadrilateral|Theorem|Questions

The radius of a circle is 50 cm. Find the angle subtends by an arc of 22 cm length at the centerof the circle.

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.

Find the angle subtended at the centre of a circle of radius 'a' by an arc of length (a pi/4)

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^(@))

Any angle subtended by a minor arc in the alternate segment is acute and any angle subtended by a major arc in the alternate segment is obtuse.

Assertion : Radian is the unit of distance. Reason : One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.