Test: Introduction To Circles - Class 9 MCQ

The sector is the region between an arc and two radii joining the center to the endpoints of the arc.
Example: In the given figure, OAB is the sector of the circle.

Concentric circles are circles with a common center. The region between two concentric circles of different radii is called an annulus.
Any two circles can be made concentric by inversion by picking the inversion center as one of the limiting points.

The angle subtented by the arc at the centre is double the angle subtented by it at any point on the circle.

A circle divides the plane on which it lies into three parts:
(i) Inside the circle, which is also called the interior of the circle.
(ii) The circle
(iii) Outside the circle, this is also called the exterior of the circle.

The circle and its interior make up the circular region.
 

Segment of a Circle: The region between a chord of a circle and its associated arc.

Diameter is the longest chord of a circle and is always twice the radius.
[∵ Diameter = 2 × Radius]

One circle measures 360 degrees. The half of the circle is called a semi-circle.
Thus, the measure of semi-circle
= 360/2 = 180 degree.

A secant of a curve is a line that intersects the curve in at least two (distinct) points.The word secant comes from the Latin word secare, meaning to cut. In the case of a circle, a secant will intersect the circle in exactly two points and a chord is the line segment determined by these two points, that is the interval on a secant whose endpoints are these points.

∠BOA = 120° (Given)
∠AOC = 60° (Linear Pair)

In triangle OAC,
OA = OC (Radii of same circle)
∠OAC = ∠ OCA = x (angle opposite to equal sides are equal)
∵ ∠A + ∠C +∠O = 180°
⇒ x + x + 60 = 180°
⇒ 2x = 120°
⇒ x =60^o

A chord is a line segment that joins two points on the circumference of a circle, and the longest chord of a circle is the diameter of the circle since the diameter passes through and contains the center of the circle.