Q3 of 12 Page 167

In the figure, PQ and XY are parallel tangents. If ∠QRT = 30°, then find the value of ∠TSY.

In the given figure,


Let O be the centre of the circle


Join OS


Let O be the centre of the circle


So ∠ SRQ = 90° [radius is perpendicular to tangent]


So ∠ SRT = 90 – 30


= 60°


∠ STR = 90° [angle in a semicircle is 90°]


∠ RSY = 90° [radius is perpendicular to tangent]


∠ RST + ∠ STR + ∠ SRT = 180° [sum of internal angles in a triangle is 180°]


∠ RST + 90 + 60 = 180


∠ RST = 180 – 150


∠ RST = 30°


∠ TSY = ∠ RSY - ∠ RST


= 90 – 30


= 60°


∴ ∠ TSY = 60°


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(i) Alternate segment of ∠BAQ.


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