In the figure, given below, P and Q are the centres of two circles intersecting at B and C ACD is a straight line. Calculate the numerical value of x .
Exercise 17 (A) | Q 32 | Page 260
Download our app for free and get started
$\angle ACB =\frac{1}{2} \angle A P B=\frac{1}{2} \times 150=75^{\circ}$
(Angle at the centre is double the angle at the circumference subtended by the same chord)
∠ACB + ∠BCD =180°
(Straight line)
⇒ ∠BCD =180° - 75° =105°
Also,$\angle B C D=\frac{1}{2}=$ reflex $\angle BQD =\frac{1}{2}\left(360^{\circ}- x \right)$
(Angle at the center is double the angle at the circumference subtended by the same chord) x
⇒ 105 = 180°
∴ x = 2 (180 ° -° ) = 2×75 = 150°
(Angle at the centre is double the angle at the circumference subtended by the same chord)
∠ACB + ∠BCD =180°
(Straight line)
⇒ ∠BCD =180° - 75° =105°
Also,$\angle B C D=\frac{1}{2}=$ reflex $\angle BQD =\frac{1}{2}\left(360^{\circ}- x \right)$
(Angle at the center is double the angle at the circumference subtended by the same chord) x
⇒ 105 = 180°
∴ x = 2 (180 ° -° ) = 2×75 = 150°
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, O is the centre of the circle and ∠ABC = 55°. Calculate the values of x and y.
- 3View SolutionIn the following figure, O is centre of the circle and ΔABC is equilateral.
Find:(i) ∠ADB, (ii) ∠AEB.
- 4View SolutionABCD is a cyclic quadrilateral in a circle with centre O. If ∠ADC = 130°; find ∠ BAC.
- 5View SolutionIn the given figure, ∠BAD = 65°, ∠ABD = 70° and ∠BDC = 45°. Find: ∠ ACB.
Hence, show that AC is a diameter.
- 6View SolutionIn the given figure, PQ is the diameter of the circle whose centre is O. Given ∠ROS = 42°, Calculate ∠RTS.
- 7View 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 - 8View SolutionIn the given figure, SP is bisector of ∠RPT and PQRS is a cyclic quadrilateral. Prove that SQ = SR .
- 9View SolutionIn the figure, given below, ABCD is a cyclic quadrilateral in which ∠BAD = 75°; ∠ABD = 58°
and ∠ADC = 77°. Find:
1. ∠BDC
2. ∠BCD
3. ∠BCA.
- 10View SolutionIn the given figure, AD is a diameter. O is the centre of the circle. AD is parallel to BC and ∠CBD = 32°.
Find: ∠BED