In the Given Figure, O is the Centre of the Circle. If ∠Cea = 30°, Find the Values of X, Y and Z. - Mathematics

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Short Note

In the given figure, O is the centre of the circle. If ∠CEA = 30°, Find the values of xy and z.

 

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Solution

It is given that, O is the centre of the circle and `angle AEC = 30°`  

We have to find the value of xy and z.

Since, angle in the same segment are equal

So  `angle AEC = angle ADC = 30°`

And z = 30°               

As angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Since  `angle AOC = 2 angle ADC`

Then,

= 2z
   = 2 × 30°
   = 60°

Since, the sum of opposite pair of angles of a cyclic quadrilateral is 180°.

z + x = 180°
= 180° − 30°
   = 150°


Hence,
x = 150°, y = 60° and z = 30°

  Is there an error in this question or solution?
Chapter 15: Circles - Exercise 15.5 [Page 102]

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RD Sharma Mathematics for Class 9
Chapter 15 Circles
Exercise 15.5 | Q 14 | Page 102

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