Question

. in a cyclic quadrilateral ABCD diagonal AC
bisects the angle C. Then prove that diagonal BD is parallel
tangent line PQ of a circle which passes through the
points A, BC and D.​

Answer 1

Proved below.

Step-by-step explanation:

Given:

Here in a cyclic quadrilateral ABCD, diagonal AC  bisects the angle C.

∠ACD=∠ACB      [1]

To prove:

BD║PQ

Proof:

Here we can see that,

∠QAD =∠ABD     [Angle in the alternate segment]

Similarly , ∠PAB =∠ADB      [Angle in the alternate segment]

Also AB is common arc and ADB and ACB are the angle in the same segment so,  

∠ADB =∠ACB

Similarly  ∠ABD =∠ACD

But ∠ACD =∠ACB             [ from Eq 1 ]

So ∠ QAD=∠ADB    [Alternate interior angle]

So BD║PQ

Hence proved.

Answer 2

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