Mathematics
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
Related Questions
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.
In the given figure, ∠ACE = 43° and ∠CAF = 62°; find the values of a, b and c.
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 cyclic quadrilateral ABCD; AD = BC, ∠BAC = 30° and ∠CBD = 70°; find :
(i) ∠BCD
(ii) ∠BCA
(iii) ∠ABC
(iv) ∠ADC