The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called a circle.
The fixed point is called the centre of the circle.
The fixed distance is called the radius of the circle.
The line segment joining the centre and any point on the circle is also called a radius of the circle. That is, ‘radius’ is used in two senses in the sense of a line segment and also in the sense of its length.
The Perimeter of the circle is called the circumference.
The line segment, joining any two points on the circumference of the circle, is called a chord.
A chord, which passes through the centre of the circle is called the diameter, and is the largest chord of the circle which is equal to two times the radius.
- A sector is a region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides.
A segment of a circle is a region in the interior of the circle enclosed by an arc and a chord.
A diameter of a circle divides it into two equal parts; each part is a semi-circle. A semi-circle is half of a circle, with the endpoints of diameter as part of the boundary.
Shaalaa.com | Circles
Two parallel chords are drawn in a circle of diameter 30.0 cm. The length of one chord is 24.0 cm and the distance between the two chords is 21.0 cm; find the length of another chord.
In the following figure, AB is the diameter of a circle with centre O and CD is the chord with length equal to radius OA.
Is AC produced and BD produced meet at point P; show that ∠APB = 60°
In the given figure ABC is an isosceles triangle and O is the centre of its circumcircle. Prove that AP bisects angle BPC .
In the given figure, O is the centre of the circle. If ∠AOB = 140° and ∠OAC = 50°; Find:
(i) ∠ACB, (ii) ∠OBC, (iii) ∠OAB, (iv) ∠CBA.
ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles.