In Fig. 16.193, two circles intersect at A and B. The centre of the smaller circle is O and it lies on the circumference of the larger circle. If ∠APB=70°, find ∠ACB.
Answers
Given : Two circles intersect at A and B. The centre of the smaller circle is O and it lies on the circumference of the larger circle and ∠APB = 70°. find ∠ACB.
To find : The value of ∠ACB.
Solution :
O is the centre of the smaller circle.
∠APB = 70°
Since, the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
∴ ∠AOB = 2 ∠APB
∠AOB = 2 × 70°
∠AOB = 140°
Since, AOBC is a cyclic quadrilateral, and Sum of Opposite pair of angles in a cyclic quadrilateral is 180° :
∠ACB + ∠AOB = 180°
∠ACB + 140° = 180°
∠ACB = 180° - 140°
∠ACB = 40°
Hence , ∠ACB is 40°,
HOPE THIS ANSWER WILL HELP YOU…..
Some questions of this chapter :
In Fig. 16.189, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC=55° and ∠BAC=45°, find ∠BCD.
https://brainly.in/question/15910512
In Fig. 16.179 ABCD is a cyclic quadrilateral. If ∠BCD=100° and ∠ABD=70°, find ∠ADB.
https://brainly.in/question/15910464
Answer:
Given : Two circles intersect at A and B. The centre of the smaller circle is O and it lies on the circumference of the larger circle and ∠APB = 70°. find ∠ACB.
To find : The value of ∠ACB.
Solution :
O is the centre of the smaller circle.
∠APB = 70°
Since, the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
∴ ∠AOB = 2 ∠APB
∠AOB = 2 × 70°
∠AOB = 140°
Since, AOBC is a cyclic quadrilateral, and Sum of Opposite pair of angles in a cyclic quadrilateral is 180° :
∠ACB + ∠AOB = 180°
∠ACB + 140° = 180°
∠ACB = 180° - 140°
∠ACB = 40°
Hence , ∠ACB is 40°,
HOPE THIS ANSWER WILL HELP YOU…..
Some questions of this chapter :
In Fig. 16.189, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC=55° and ∠BAC=45°, find ∠BCD.
https://brainly.in/question/15910512
In Fig. 16.179 ABCD is a cyclic quadrilateral. If ∠BCD=100° and ∠ABD=70°, find ∠ADB.
https://brainly.in/question/15910464