Inscribed Angle Theorem
The measure of an inscribed angle is half of the measure of the arc intercepted by it.
Given `:` In a circle with centre O, `/_BAC ` is inscribed in an arc BAC. `/_BAC` intercepts are BXC of the circle.
To prove `: m /_BAC = (1)/(2) ` m ( arc BXC ) .

Corollaries of inscribed angle theorem : Angle inscribed in the same arc arc contruent Given : (1) A circle with centre O (2) /_ABD and /_ACD are inscribed in arc ABC and intercepts arc APD. To prove : /_ABD ~= /_ACD

In the figure, O is the centre of the circle. Seg AC is the diameter /_ ABC is inscribed in arc ABC and intercepts arc AMC then prove /_ ABC = 90^(@)

/_ACB is inscribed in arc ACB of a circle with centre O . If /_ACB= 65^(@) , find m ( arc ACB ) .

Theorem of angle between tangent and secant If an angle has its vertex on the circle, its one side touches the circle and the other intersects the circle in one more point, then the measure of the angle is half the measure of its intercepted arc . Given : Let O be the centre of the circle. Line DBC is tangent to the circle at point B. Seg BA is a chord of the circle. Point X of the circle is on C side of line BA and point Y of the circle is on D side of line BA. To prove : m /_ ABC = (1)/(2) m (arc AXB) .

BC is a chord with centre O. A is a point on an arc BC . Prove that: ∠BAC−∠OBC= 90^@ .

In a circle with radius 3 cm an arc of length 1 cm subtends an angle of measure ……… at the centre of the circle.

angleACB is inscribed in area ACB of a circle with centre O . If angleACB=65^(@) , find m(arc ACB).

The measure of a minor arc PXQ of a circle with centre O is 110^@ . What is the measure of the major arc PYQ ?