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In the Given Figure, O is the Centre of the Circle and ∠Abc = 55°. Calculate the Values of X and Y. - ICSE Class 10 - Mathematics

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ConceptArc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle

Question

In the given figure, O is the centre of the circle and ∠ABC = 55°. Calculate the values of x and y.

Solution

∠AOC = 2 ∠ABC = 2 × 55°
(Angle at the centre is double the angle at the circumference subtended by the same chord)
∴ x = 110°
ABCD is cyclic quadrilateral
∴ ∠ADC +∠ ABC = 180°
(pair of opposite angles in a cyclic quadrilateral are supplementary
⇒  y = 180° - 55° = 125°

 

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Solution In the Given Figure, O is the Centre of the Circle and ∠Abc = 55°. Calculate the Values of X and Y. Concept: Arc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle.
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