Meritnation Experts,please answer these question as soon as possible with explanation:
a.Prove that the quadrilateral formed(if possible) by the internal angle bisectors of any quadrilateral is cyclic.
b.ABCD is a cyclic quadrilateral whose diagonals intersect at a point E.If angle DBC=70 degree,angle BAC=30 degree,find angle BCD.Further if AB=BC,find angle ECD
(a) Here is the link for answer to your query.
Given: ∠BAC = and ∠DBC =
∠DBC = ∠DAC = (angles in the same segment made by chord CD)
∠A = ∠DAC + ∠BAC = + =
Since opposite angles of a cyclic quadilateral are supplementary,
∠A + ∠BCD =
If AB = BC,
∠ACB = ∠BAC =
∠ECD = ∠BCD – ∠ACB =