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.

https://www.meritnation.com/ask-answer/question/prove-that-the-quadrilateral-formed-if-possible-by-the-int/circles/3867182

 

(b)

 

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 =

∠BCD =

If AB = BC,

∠ACB = ∠BAC =

∠ECD = ∠BCD – ∠ACB =

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