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11 Plus Circle

11 Plus Circle

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Circle:

A circle is a locus of all points which are at the same distance from the fixed point. This distance from the centre to each point is called the radius.

Different parts of a circle:

Centre: Centre of a circle is the point that is equidistant from all points of the circle.

Radius: A line from the centre of a circle to the circumference of a circle.

Diameter: Diameter is a line that passes through the centre of the circle and whose endpoints lie on the circle.

Diameter (d) = 2 x radius

Chord: A Chord is a line segment that connects two points present in the circle's circumference. If the chord passes through the centre of the circle, then it is called the diameter.

Tangent: A line that touches the circumference of a circle at any one point is called a Tangent.

If any two circles are given which do not intersect, then both circles can have common tangents, as shown below:

Arc (Major and Minor): A small part of the circumference of a circle.

Minor Arc: An arc that is less than half of the circle is called its Minor arc. In the above diagram PQ (red colour arc) is called Minor arc.

Major Arc: An arc that is more than half of the circle is called its Major arc. In the above diagram, QP (blue colour arc) is called Major arc.

Sector (Major and Minor): A part of the circle enclosed by two radii (r1 and r2) of the circle. A sector means a portion of the circle. The arc is just part of the circumference, but the sector is part of the area.

Segment (Major or Minor): Area between the chord and circumference of a circle is called a circle segment.

Area of a Circle:

The amount of space occupied by the circle is defined as the area of a circle.

Where r= radius

d=diameter=2r

Circumference of the Circle:

Distance around the circle is defined as the circumference of a circle.

Where r= radius

d=diameter

d=2r

Semi-Circle:

A semi-circle is formed when the circle is divided into two parts.

Area of Semicircle:

 The area of a semi-circle is equal to half of the area of the circle.

Circumference of Semicircle:

The circumference or perimeter of a semi-circle is equal to half of the circumference of the circle.

Example1:

Find the area and circumference of a circle with a radius of 5cm.

Solution:

Example2:

Find the minor arc length AB and area of the sector OAB of the circle given below.

Example 3:

Example 4:

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