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प्रश्न
In the figure, given alongside, AB || CD and O is the centre of the circle. If ∠ADC = 25°; find the angle AEB. Give reasons in support of your answer.
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उत्तर
Join AC and BD
∴ ∠CAD = 90° and ∠CBD = 90°
(Angle in a semicircle is a right angle)
Also, AB || CD
∴ ∠BAD = ∠ADC = 25° ...(Alternate angles)
∠BAC = ∠BAD + ∠CAD
= 25° + 90°
= 115°
∴ ∠ADB = 180° – 25° – ∠BAC
= 180° – 25° – 115°
= 40°
(Pair of opposite angles in a cyclic quadrilateral are supplementary)
Also, ∠AEB = ∠ADB = 40°
(Angle subtended by the same chord on the circle are equal)
संबंधित प्रश्न
In the given figure, ∠BAD = 65°, ∠ABD = 70°, ∠BDC = 45°
1) Prove that AC is a diameter of the circle.
2) Find ∠ACB
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Calculate:
- ∠DAB,
- ∠DBA,
- ∠DBC,
- ∠ADC.
Also, show that the ΔAOD is an equilateral triangle.
Prove that the perimeter of a right triangle is equal to the sum of the diameter of its incircle and twice the diameter of its circumcircle.
Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.
The following figure shows a circle with PR as its diameter. If PQ = 7 cm and QR = 3RS = 6 cm, find the perimeter of the cyclic quadrilateral PQRS.
In the following figure, AD is the diameter of the circle with centre O. chords AB, BC and CD are equal. If ∠DEF = 110°, Calculate: ∠FAB.
In Fig, Chord ED is parallel to the diameter AC of the circle. Given ∠CBE = 65°, Calculate ∠ DEC.
In the figure, ∠DBC = 58°. BD is diameter of the circle.
Calculate:
- ∠BDC
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In the figure given alongside, AD is the diameter of the circle. If ∠ BCD = 130°, Calculate: (i) ∠ DAB (ii) ∠ ADB.
In the given figure, AC is the diameter of the circle with center O.
CD is parallel to BE.
∠AOB = 80° and ∠ACE = 20°
Calculate:
- ∠BEC
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