Advertisements
Advertisements
Question
In the given figure, two circles intersect at A and B. The centre of the smaller circle is Oand it lies on the circumference of the larger circle. If ∠APB = 70°, find ∠ACB.
Advertisements
Solution
Consider the smaller circle whose centre is given as ‘O’.
The angle subtended by an arc at the centre of the circle is double the angle subtended by the arc in the remaining part of the circle.
So, here we have
`angle AOB = 2 angle APB `
= 2 (70°)
`angle AOB = 140°`
Now consider the larger circle and the points ‘A’, ‘C’, ‘B’ and ‘O’ along its circumference. ‘ACBO’ form a cyclic quadrilateral.
In a cyclic quadrilateral it is known that the opposite angles are supplementary, meaning that the opposite angles add up to 180°.
`angleAOB + angle ACB` = 180°
`angle ACB = 180° - angle AOB`
`= 180° - 140°`
`angle ACB = 40°`
Hence ,the measure of` ` angle ACB ` is 40° .
APPEARS IN
RELATED QUESTIONS
Given an arc of a circle, complete the circle.
In the below fig. O is the centre of the circle. Find ∠BAC.
If O is the centre of the circle, find the value of x in the following figure
If O is the centre of the circle, find the value of x in the following figure
O is the circumcentre of the triangle ABC and OD is perpendicular on BC. Prove that ∠BOD = ∠A.
In the given figure, it is given that O is the centre of the circle and ∠AOC = 150°. Find ∠ABC.
In the given figure, O is the centre of the circle, prove that ∠x = ∠y + ∠z.
Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half the hypotenuse.
In the given figure, two congruent circles with centres O and O' intersect at A and B. If ∠AOB = 50°, then find ∠APB.
In the following figure, ∠ACB = 40º. Find ∠OAB.
