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
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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