Advertisements
Advertisements
Question
An equilateral triangle ABC is inscribed in a circle with centre O. The measures of ∠BOCis
Options
30°
60°
90°
120°
Solution
120°
We are given that an equilateral ΔABC is inscribed in a circle with centre O. We need to find ∠BOC
We have the following corresponding figure:
We are given AB = BC = AC
Since the sides AB, BC, and AC are these equal chords of the circle.
So, the angle subtended by these chords at the centre will be equal.
Hence
`angleAOB + angleBOC + angleAOC = 360`
`angleBOC + angleBOC + angleBOC = 360`
`3angleBOC = 360`
`angleBOC = 360/3`
`angleBOC = 120°`
APPEARS IN
RELATED QUESTIONS
A chord of a circle of radius 10 em subtends a right angle at its centre. The length of the chord (in em) is
`(A) 5sqrt 2`
`(B) 10 sqrt2`
`(C)5/sqrt2`
`(D) 10sqrt 3`
Fill in the blank:
A point whose distance from the centre of a circle is greater than its radius lies in ..................... of the circle.
The perimeter (in cm) of a square circumscribing a circle of radius a cm, is
In the given figure, O is the centre of the circle. If ∠BOD = 160°, find the values of x and y.
The radius of a circle is 6 cm. The perpendicular distance from the centre of the circle to the chord which is 8 cm in length, is
If AB, BC and CD are equal chords of a circle with O as centre and AD diameter, than ∠AOB =
If O is the centre of the circle, find the value of x in each of the following figures
In the figure, segment PQ is the diameter of the circle with center O. The tangent to the tangent circle drawn from point C on it, intersects the tangents drawn from points P and Q at points A and B respectively, prove that ∠AOB = 90°
In the given figure, if ZRPS = 25°, the value of ZROS is ______
In the given figure, O is the centre of the circle. Name a chord, which is not the diameter of the circle.
