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.

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.

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.

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

Theorem:-6Any angle subtended by minor arc in the alternate segment is acute and any angle subtended by major arc in the alternate segment is obtuse.

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

Equal chords of a circle subtend equal angles at the centre.

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^(@))

Find tge degree measure of the angle subtended at the centre of a circle of diameter 60 cm by an arc of length 16.5 cm.