Advertisements
Advertisements
प्रश्न
In the following figure, ∠OAB = 30º and ∠OCB = 57º. Find ∠BOC and ∠AOC.
Advertisements
उत्तर
Given, ∠OAB = 30° and ∠OCB = 57°
In ΔAOB, AO = OB ...[Both are the radius of a circle]
⇒ ∠OBA = ∠BAO = 30° ...[Angles opposite to equal sides are equal]
In ΔAOB,
⇒ ∠AOB + ∠OBA + ∠BAO = 180° ...[By angle sum property of a triangle]
∴ ∠AOB + 30° + 30° = 180°
∴ ∠AOB = 180° – 2(30°)
= 180° – 60°
= 120° ...(i)
Now, in ΔAOB,
OC = OB ...[Both are the radius of a circle]
⇒ ∠OBC = ∠OCB = 57° ...[Angles opposite to equal sides are equal]
In ΔOCB,
∠COB + ∠OCB + ∠CBO = 180° ...[By angle sum property of triangle]
∴ ∠COB = 180° – (∠OCB + ∠OBC)
= 180° – (57° + 57°)
= 180° – 114°
= 66° ...(ii)
From equation (i), ∠AOB = 120°
⇒ ∠AOC + ∠COB = 120°
⇒ ∠AOC + 66° = 120° ...[From equation (ii)]
∴ ∠AOC = 120° – 66° = 54°
APPEARS IN
संबंधित प्रश्न
Two concentric circles are of radii 6.5 cm and 2.5 cm. Find the length of the chord of the larger circle which touches the smaller circle.
In Fig 2, a circle touches the side DF of ΔEDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm, then the perimeter of ΔEDF (in cm) is:
Find the length of the chord of a circle in the following when:
Radius is 1. 7cm and the distance from the centre is 1.5 cm
Find the area of a circle of radius 7 cm.
State, if the following statement is true or false:
Every diameter bisects a circle and each part of the circle so obtained is a semi-circle.
In the table below, write the names of the points in the interior and exterior of the circle and those on the circle.
| Diagram | Points in the interior of the circle |
Points in the exterior of the circle |
Points on the circle |
 |
The diameter of the circle is 52 cm and the length of one of its chord is 20 cm. Find the distance of the chord from the centre
Find the diameter of the circle
Radius = 6 cm
In the figure, O is the centre of a circle, AB is a chord, and AT is the tangent at A. If ∠AOB = 100°, then ∠BAT is equal to ______
If a chord AB subtends an angle of 60° at the centre of a circle, then the angle between the tangents at A and B is ______
