Q. 34.0( 9 Votes )
In the figure, PQ and XY are parallel tangents. If ∠QRT = 30°, then find the value of ∠TSY.

Answer :
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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