In the following figure, O is centre of the circle and ΔABC is equilateral.
Find:(i) ∠ADB, (ii) ∠AEB.
Find:(i) ∠ADB, (ii) ∠AEB.
Exercise 17 (A) | Q 11 | Page 258
Download our app for free and get started
Since ∠ACBand ∠ADBare in the same segment,
∠ADB = ∠ACB = 60°
Join OA and OB
Here, ∠AOB =2 ∠ACB = 2×60° = 120°
$\angle A E B=\frac{1}{2} \operatorname{Reflex}(\angle AOB )=\frac{1}{2}\left(360^{\circ}-120^{\circ}\right) 120^{\circ}$
(Angle at the centre is double the angle at the circumference subtended by the same chord)
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionIn the following figure, AD is the diameter of the circle with centre O. chords AB, BC and CD are equal. If ∠DEF = 110°, Calculate: ∠AEF
- 2View SolutionIn the given figure, O is the centre of the circle. ∠OABand ∠OCB are 30° and 40°
respectively. Find ∠AOC . Show your steps of working.
- 3View SolutionThe figure given below, shows a circle with centre O. Given: ∠ AOC = a and ∠ ABC = b.
1. Find the relationship between a and b.
2. Find the measure of angle OAB, if OABC is a parallelogram.
- 4View SolutionABCD is a cyclic quadrilateral in which AB is parallel to DC and AB is a diameter of the circle. Given ∠BED = 65°; Calculate:
(i) ∠DAB, (ii) ∠BDC
- 5View SolutionIn the given figure, O is the centre of the circle and ∠ABC = 55°. Calculate the values of x and y.
- 6View SolutionIn the given figure, AD is a diameter. O is the centre of the circle. AD is parallel to BC and ∠CBD = 32°.
Find: ∠AOB - 7View SolutionIn the given figure, RS is a diameter of the circle. NM is parallel to RS and ∠MRS = 29°.
Calculate : ∠ NRM
- 8View SolutionIn the given figure, AB = BC = CD and ∠ABC = 132° . Calcualte: ∠ COD.
- 9View SolutionIn the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight sided polygon inscribed in the circle with centre O. Calculate the sizes of:
(i) ∠AOB, (ii) ∠ACB (iii) ∠ABC
- 10In the figure, AB is a common chord of the two circles. If AC and AD are diameters; prove that D, B, and C are in a straight line. $O_1$ and $O_2$ are the centers of two circles.View Solution
