In the given figure, `AB` is the diameter of a circle with centre `O` and `AT` is a tangent. If `/_AOQ=58^(@)`, find `/_ATQ`.

Explanation

`/_AOQ=58^(@)`
`implies/_ABQ=(1)/(2)/_AOQ=29^(@)` [`:' ` the angle subtended by an arc at the centre is double the angle subtened by it at any point on the remaining part of the circle]
`implies/_ABT=29^(@)`.
Now, `AT` is a tangent at `A` and `OA` is the radius through the point of contact `A`.
`:.OAbotAT`, i.e., `/_OAT=90^(@)implies/_BAT=90^(@)`.
In `DeltaBAT`, we have
`/_BAT+/_ABT+/_ATB=180^(@)`
`implies90^(@)+29^(@)+/_ATB=180^(@)implies/_ATB=61^(@)`.
`:./_ATQ=/_ATB=61^(@)`.