P and Q are the middle points of two chords not diameters AB and AC respectively of a circle with ce...........

Quantitative Aptitude ( CCS) Geometry

P and Q are the middle points of two chords (not diameters) AB and AC respectively of a circle with centre at a point O. the lines OP and OQ are produced to meet the circle respectively at the points R and S. T is any point on the major arc between the points R and S of the circle. If ∠BAC = 32°, ∠RTS = ?

32°

74°

106°

64°

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Explanation:

P and Q are mid points of AB and AC so OP and OS will be perpendicular at AB and AC respectively.
∴ ∠APO = ∠AQO = 90°
⇒ ∠ROS = 180° – 32°
∠ROS = 148°
∠RTS = 1/2 ∠ROS
∠RTS = 74°