In the given figure, `PA` is a tangent from an external point `P` to a circle with centre `O`. If `/_POB=115^(@)`, find `/_APO`.

Explanation

We know that the tangent at a point to a circle is perpendicular to the radius passing through the point of contact.
`:. /_OAP=90^(@)`
Now, `/_AOP+/_BOP=180^(@)`
`implies/_AOP=180^(@)-/_BOP=180^(@)-115^(@)=65^(@)`
Now, `/_OAP+/_AOP+/_APO=180^(@)`[sum of angles of a triangle is `180^(@)`]
`implies/_APO=180^(@)-(/_OAP+/_AOP)=180^(@)-(90^(@)+65^(@))=25^(@)`.