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In the Figure, Given Below, O is the Centre of the Circumcircle of Triangle Xyz. Tangents at X and Y Intersect at Point T. Given ∠Xty = 80°, and ∠Xoz = 140°, Calculate The Value of ∠Zxy. - Mathematics

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Question

In the figure, given below, O is the centre of the circumcircle of triangle XYZ.

Tangents at X and Y intersect at point T. Given ∠XTY = 80°, and ∠XOZ = 140°, calculate the  value of ∠ZXY.

Solution

In the figure, a circle with centre O, is the circum circle of triangle XYZ.
`∠`XOZ =140°
Tangents at X and Y intersect at point T, such that `∠`XTY = 80°
∴ `∠`XOY = 180° - 80° =100°
But, `∠`XOY+ `∠`YOZ +`∠`ZOX = 360° [Angles at a point]
⇒ 100° + `∠`YOZ +140° = 360°
⇒ 240°  + `∠`YOZ = 360°
⇒ `∠`YOZ = 360° - 240°
⇒  `∠`YOZ  = 120
Now arc YZ subtends `∠`YOZat the centre and `∠`YXZat the remaining part of the circle.
∴  `∠`YOZ = 2`∠`YXZ
` ⇒ ∠YXZ =1/2 ∠YOZ`
⇒  `∠YXZ  = 1/2 xx120° =  60°`

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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 18: Tangents and Intersecting Chords
Exercise 18 (C) | Q: 40 | Page no. 287
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In the Figure, Given Below, O is the Centre of the Circumcircle of Triangle Xyz. Tangents at X and Y Intersect at Point T. Given ∠Xty = 80°, and ∠Xoz = 140°, Calculate The Value of ∠Zxy. Concept: Tangent Properties - If a Chord and a Tangent Intersect Externally, Then the Product of the Lengths of Segments of the Chord is Equal to the Square of the Length of the Tangent from the Point of Contact to the Point of Intersection.
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