In the given figure, AB is a diameter of the circle C(O,r) and the radius OD is perpendicular to AB. If C is anypoint on `hat (DB)` , find `/_ BAD` and `/_ ACD`

Explanation

OA=OD=r `implies /_OAD =/_ ODA` …..(i)
In `Delta ` OAD, we have
`/_ OAD + /_ ODA + /_ AOD = 180^(@)` [ sum of the `Delta ` of a triangle]
`implies 2 /_ OAD + 90^(@) =180^(@) [ /_ AOD =90^(@)` and using (i) ]
`implies /_OAD = 45^(@)`
`gt /_ OAD = 45^(@) [ :' /_BAD = /_ OAD ]`.
Similarly , by taking `Delta OBD`, we can prove that `/_ ABD = 45^(@)` .
`:. /_ ACD = /_ ABD =45^(@) ` [ angles in the same segments ].
Hence, `/_ BAD = 45^(@) ` and `/_ ACD = 45^(@)`