Q,R,S,T are four points
on the circumference of a circle. QT is the perpendicular bisector of RS. PQ is
a tangent drawn to the circle from an external point P. If angle(SQP) = 20,
find angle(TRS).
Answer: 70 degrees
Explanation:
Consider the diagram
below.
QT is the perpendicular bisector of a chord RS. Hence QT has to pass through the centre of the circle.
Angle(OQP) = 90 as the
radius of a circle meets a tangent perpendicularly at the point of tangency.
Angle(SQP) = 20. Hence
angle(SQO) = 70.
Now for chord TS,
angle(TQS) = angle(TRS) as they are in the same segment.
Hence angle(TRS) = 70.