Angle Subtended by an Arc of a Circle

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.

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.

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

i) The radius of a circle is 40cm. Find the angle subtend by an arc of 22 cm at the center of circle in degrees.

In the figure,AB and CD are two chords of a circle,interacting each other at a point E. Prove that /_AEC=1/2 (angle subtended by arc CXA.at the centre + angle subtended by arc DYB at the centre).

A piece of wire of length 33 cm is bent into an arc of a circle of radius 14 cm. What is the angle subtended by the arc at the centre 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.