Math, asked by oplakas5, 3 months ago

A,B,C are any points on the circle with cemtre O. if m are (BC)=110° and m arc (AB)=125°, find measure of arc (ABC)​

Answers

Answered by d200876
0

Answer:

115*

Step-by-step explanation:

Take any point P on the circumference of the circle as shown.

Join AP and CP.

∵ABC subtends ∠AOC at centre O and ∠APC at any point P on the circumference of the circle.

∴∠AOC=2∠APC ...[∵ Angle subtended by an arc at the centre is twice the angle at the circumference]

∴∠APC=  

2

1

​  

∠AOC[∵AOC=130  

]

⟹  

2

1

​  

×130  

=65  

.

∵ ABCP is a cycle quadrilateral,

⟹∠APC+∠ABC=180  

 ...[∵ sum of opposite angles of a cyclic quadrilateral is 180  

]

⟹65  

+∠ABC=180  

 

∴∠ABC=180  

−65  

=115  

.

Hence, option B is correct.

Answered By

Divyanshu

Lived in Naraina

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