In the given figure, AC is the diameter of circle, centre $\mathrm{O} . \mathrm{CD}$ and BE are parallel. Angle $\mathrm{AOB}=80^{\circ}$ and angle $\mathrm{ACE}=$ $10^{\circ}$. Calculate : Angle BCD
Exercise 17 (A) | Q 44.2 | Page 261
Download our app for free and get started
DC || EB
∴ DCE = ∠BEC = 50° (Alternate angles)
∴ ∠ AOB = 80°
$\Rightarrow \angle ACB =\frac{1}{2} \angle AOB =40^{\circ}$
(Angle at the center is double the angle at the circumference subtended by the same chord) We have,
∠BCD = ∠ACB + ∠ACE + ∠DCE = 40° +10°+ 50° = 100°
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 figure, ∠BAD = 65° , ∠ABD = 70° , ∠BDC = 45°
(i) Prove that AC is a diameter of the circle
(ii) Find ∠ACB
- 2View SolutionIn the given figure, the centre O of the small circle lies on the circumference of the bigger circle. If ∠APB = 75° and ∠BCD = 40°, find : ∠ADB
- 3View SolutionIn the following figure, O is centre of the circle and ΔABC is equilateral.
Find:(i) ∠ADB, (ii) ∠AEB.
- 4View SolutionAB is a diameter of the circle APBR as shown in the figure. APQ and RBQ are straight lines. Find: ∠ BPR
- 5View SolutionIn the figure, ∠DBC = 58°. BD is a diameter of the circle. Calculate : ∠BDC
- 6View 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.
- 7View SolutionIn the given figure, ∠BAD = 65°, ∠ABD = 70° and ∠BDC = 45°. Find: ∠ ACB.
Hence, show that AC is a diameter.
- 8View SolutionIn the given figure, O is the centre of the circle. If ∠AOB = 140° and ∠OAC = 50°; Find:
(i) ∠ACB, (ii) ∠OBC, (iii) ∠OAB, (iv) ∠CBA.
- 9View SolutionIn the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and ∠DCB = 120°.
Calculate : ∠DAB
Also show that the ΔAOD is an equilateral triangle .
- 10View SolutionIn the given figure, RS is a diameter of the circle. NM is parallel to RS and ∠MRS = 29°.
Calculate : ∠ NRM