# 7th Grade Math Circles

A circle is a simple closed shape where all points have the same distance from the centre. The centre of a circle is the centre point in a circle, from which all the distances to the points on the circle are equal. The radius is the distance from the centre to any point on the circle. The diameter of the circle is defined as the distance across the circle. The length of any chord passing through the centre is called the diameter of the circle. It is twice the radius.

## Important points of the circle

• The distance around the outside of the circle is called the circumference of the circle.
• Circumference of the circle = 2πr.
• Area of circle = π * (radius)2 = π * r= πr2
• The circles are said to be congruent if they have equal radii.
• Equal chords of a circle subtend equal angles at the centre.
• The radius drawn perpendicular to the chord bisects the chord.
• Circles having different radii are similar.
• The chords that are equidistant from the centre are equal in length.
• The distance from the centre of the circle to the longest chord (diameter) is zero.

## Circle Example

Here are a few examples of grade 7 circle problems.

1.    Find the circumference of the circles with a radius of 14 cm (Take π = 22/7)

Ø  Circumference of the circle = 2πr

Ø  = 2 * 22/7 * 14

Ø  = 2 * 22 * 2

Ø  = 88 cm

2. Find the area of the following circles with a radius of 5 cm (Take π = 22/7)

Ø  Area of circle = πr2

Ø  = π * r * r = 22/7 * 5 * 5

Ø  = (22 * 25)/7

Ø  = 550/7mm2

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## Sum Up

Studying grade 7 circles help students to develop a robust understanding of basic concepts related to circles and their components.

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