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:-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.

The angle subtended by a minor arc in its alternate segment is…………….

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.

Minor and major arcs

Which of the following can be the angle subtended by a minor arc at the centre?

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.

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 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 chord of a circle is sqrt(3) times its radius. The angle subtended by this chord at the minor arc is k times the angle subtended at the major arc. What is the value of k ?

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