In the given figure, `PQ` is a tangent to a circle with centre `O`. `A` is the point of contact. If `/_PAB=67^(@)`, then the measure of `/_AQB` is

Options

A. `73^(@)`
B. `64^(@)`
C. `53^(@)`
D. `44^(@)`

Explanation

`/_BAC=90^(@)` [angle in a semicircle]
`/_PAB+/_BAC+/_CAQ=180^(@)implies/_CAQ=180^(@)-(90^(@)+67^(@))=23^(@)`.
`/_ACB=/_PAB=67^(@)` [angle in alternate segments]
`/_ACB+/_ACQ=180^(@)` [linear pair]
`implies/_ACQ=180^(@)-67^(@)=113^(@)`.
Now, `/_CAQ+/_ACQ+/_AQC=180^(@)` [in `DeltaACQ`]
`implies/_AQC=180^(@)-(23^(@)+113^(@))=44^(@)implies/_AQB=44^(@)`.