- 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 given figure, SP is bisector of ∠RPT and PQRS is a cyclic quadrilateral. Prove that SQ = SR .
In a cyclic – quadrilateral PQRS, angle PQR = 135°. Sides SP and RQ produced meet at point A : whereas sides PQ and SR produced meet at point B.
If ∠A : ∠B = 2 : 1; find angles A and B.
ABCD is a cyclic quadrilateral. Sides AB and DC produced meet at point E; whereas sides BC and AD produced meet at point F. If ∠DCF : ∠F : ∠E = 3 : 5 : 4, Find the angles of the cyclic quadrilateral ABCD.
ABCD is a cyclic quadrilateral in which ∠DAC = 27° ; ∠DBA = 50° and ∠ADB = 33°. Calculate:
(i) ∠DBC, (ii) ∠DCB, (iii) ∠CAB
In the given figure PQRS is a cyclic quadrilateral PQ and SR produced meet at T
1) Prove ΔTPS ~ ΔTRQ.
2) Find SP if TP = 18 cm, RQ = 4 cm and TR = 6 cm
3) Find the area of quadrilateral PQRS if the area of ΔPTS = 27 cm2.
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