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A B C D is a cyclic quadrilateral whos...

`A B C D` is a cyclic quadrilateral whose diagonals `A C\ a n d\ B D` intersect at `Pdot` If `A B=D C ,` prove that:
(i)` P A B\ cong P D C`
(ii)`P A=P D\ a n d\ P C=P B` (iii) `A D|\| B C`

Text Solution

Verified by Experts

`ABCD` is a cyclic quadrilateral
so `AC = BD =` Diameter of Circle
so `AC` and `BD` will intersect at `O` center of circle
That means `P` and `O` are same point
`PA = PD =` radius
`PC = PB =` Radius
`AB = DC`
given
`/_\ APAB = /_\PCD`
`/_DCP = /_BAP and /_CDP = /_ABD`
`=> AB || DC`
Hence proved.
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