Advertisements
Advertisements
प्रश्न
An equilateral triangle ABC is inscribed in a circle with centre O. The measures of ∠BOCis
पर्याय
30°
60°
90°
120°
Advertisements
उत्तर
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
संबंधित प्रश्न
Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ.
In the following figure, AB is the diameter of a circle with centre O and CD is the chord with length equal to radius OA.
Is AC produced and BD produced meet at point P; show that ∠APB = 60°
In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, find the lengths of AD, BE and CF.
In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 3 cm such that the segments BD and DC into which BC is divided by the point of contact D, are of lengths 6 cm and 9 cm respectively. If the area of ΔABC = 54 cm2 then find the lengths of sides AB and AC.
A chord of a circle of radius 14 cm subtends an angle of 120° at the centre. Find the area of the corresponding minor segment of the circle. `[User pi22/7 and sqrt3=1.73]`
In the given figure, ABC is a right triangle right-angled at B such that BC = 6 cm and AB = 8 cm. Find the radius of its incircle.
The point of concurrence of all angle bisectors of a triangle is called the ______.
Can the length of a chord of a circle be greater than its diameter ? Explain.
If O is the center of the circle in the figure alongside, then complete the table from the given information.
The type of arc
| Type of circular arc | Name of circular arc | Measure of circular arc |
| Minor arc | ||
| Major arc |
In figure, chords AC and DE intersect at B. If ∠ABE = 108°, m(arc AE) = 95°, find m(arc DC).
