Mathematics
In the adjoining figure, if O is the centre of the circle then the value of x is
18°
20°
24°
36°
Answer
From figure,
∠ADB = ∠ACB = 2x (∵ ∵ angles in same segment are equal.)
Join OA as shown in the figure below:
Arc AB subtends ∠AOB at centre and ∠ADB at remaining part of circle.
∠AOB = 2∠ADB = 2(2x) = 4x (∵ angle subtended at centre is double the angle subtended at remaining part of circle.)
In △OAB,
OA = OB (Radius of the circle.)
So, △OAB is an isosceles triangle with ∠OBA = ∠OAB (∵ angles opposite to equal sides are equal.)
∠OAB = 3x.
Since, sum of angles in a triangle = 180°.
⇒ ∠OAB + ∠OBA + ∠AOB = 180°
⇒ 3x + 3x + 4x = 180°
⇒ 10x = 180°
⇒ x = 18°
Hence, Option 1 is the correct option.
Related Questions
In the adjoining figure, O is the centre of the circle. If ∠BAO = 60°, then ∠ADC is equal to
30°
45°
60°
120°
From a point which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is
60 cm2
65 cm2
30 cm2
32.5 cm2
In the adjoining figure, O is the centre of the circle. If the length of the chord PQ is equal to the radius of the circle, then ∠PRQ is
60°
45°
30°
15°
In the adjoining figure, PQ and PR are tangents from P to a circle with centre O. If ∠POR = 55°, then ∠QPR is
35°
55°
70°
80°
