Mathematics
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.
Related Questions
In cyclic quadrilateral ABCD; AD = BC, ∠BAC = 30° and ∠CBD = 70°; find :
(i) ∠BCD
(ii) ∠BCA
(iii) ∠ABC
(iv) ∠ADC
In the given figure, AB is the diameter of a circle with center O. If chord AC = chord AD, prove that :
(i) arc BC = arc DB
(ii) AB is the bisector of ∠CAD.
Further, if the length of arc AC is twice the length of arc BC, find :
(a) ∠BAC
(b) ∠ABC
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.
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
