- Opposite Angles of a Cyclic Quadrilateral Are Supplementary
- The Exterior Angle of a Cyclic Quadrilateral is Equal to the Opposite Interior Angle (Without Proof)
D and E are points on equal sides AB and AC of an isosceles triangle ABC such that AD = AE. Prove that the points B, C, E and D are concyclic.
In the figure given, O is the centre of the circle. `angle DAE = 70^@`, Find giving suitable reasons the measure of:
1) `angle BCD`
2) `angle BOD`
3) `angle OBD`
In the following figure, ABCD is a cyclic quadrilateral in which AD is parallel to BC.
If the bisector of angle A meets BC at point E and the given circle at point F, Prove that:
(i) EF = FC (ii) BF = DF
In a cyclic quadrilateral ABCD, the diagonal AC bisects the angle BCD. Prove that the diagonal BD is parallel to the tangent to the circle at point A.
The given figure shows a semi-circle with centre O and diameter PQ. If PA = AB and ∠BCQ =140°; Find measures of angles PAB and AQB. Also, show that AO is parallel to BQ.
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