In the Given Figure, Ab and Cd Are Diameters of a Circle with Centre O. If ∠Obd = 50°, Find ∠Aoc. - Mathematics

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Short Note

In the given figure, AB and CD are diameters of a circle with centre O. If ∠OBD = 50°, find ∠AOC.

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Solution

It is given that, AB and CD are diameter with center O and `angleOBD = 50°`

We have to find `angle AOC` 

Construction: Join the point A and D to form line AD

Clearly arc AD subtends`angle ABD = 50°`  at B and `angleAOD`  at the centre.

Therefore, 

\[\angle AOD = 2\angle ABD = 100° \]         …… (1)

Since CD is a straight line then

\[\angle DOA + \angle AOC = 180° \left( \text{ Linear pair } \right)\]
`angle AOC = 180° - 100°`
             = 80°
Hence `angle AOC = 80°

 

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Chapter 15: Circles - Exercise 15.5 [Page 101]

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RD Sharma Mathematics for Class 9
Chapter 15 Circles
Exercise 15.5 | Q 7 | Page 101

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