# RS Aggarwal Class-9 Chord Properties of Circle ICSE Maths Solutions

**RS Aggarwal Class-9 Chord Properties** of Circle ICSE Mathematics Solutions Goyal Brothers Prakashan Chapter-13. We provide step by step Solutions of Exercise / lesson-13 **Chord Properties** of Circle for ICSE** Class-9 RS** Aggarwal Mathematics .

Our Solutions contain all type Questions with Exe-13 to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board Class-9 Mathematics.

**RS Aggarwal Class-9 Chord Properties** of Circle ICSE Mathematics Solutions Goyal Brothers Prakashan Chapter-13

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**Notes **on Chord Properties of Circle

Some of the important properties of the circle are as follows:

- The circles are said to be congruent if they have equal radii
- The diameter of a circle is the longest chord of a circle
- Equal chords and equal circles have equal circumference
- The radius drawn a perpendicular to the chord bisects the chord
- Circles having different radius are similar
- A circle can circumscribe a rectangle, trapezium, triangle, square, kite
- A circle can be inscribed inside a square, triangle and kite
- 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
- The perpendicular distance from the centre of the circle decreases when the length of the chord increases

## Chord of a Circle Definition

The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle. It should be noted that the diameter is the longest chord of a circle which passes through the center of the circle.

**Theorem on Chord Properties**

Theorem 1: Equal Chords Equal Angles Theorem

Statement: Chords which are equal in length subtend equal angles at the center of the circle.

Theorem 2: Equal Chords Equidistant from Center Theorem

Statement: Equal chords of a circle are equidistant from the center of the circle.

Theorem 3: “Chords of a circle, which are at equal distances from the centre are equal in length is also true.”

Theorem 4: **“**A straight line passing through the centre of a circle to bisect a chord is perpendicular to the chord.”

Theorem 5 Circle Geometry: Converse Rule

A line segment that passes through the circle’s centre bisects the chord will be perpendicular to the chord.

**RS Aggarwal Class-9 Chord Properties** of Circle ICSE Mathematics Solutions Goyal Brothers Prakashan **Exercise-13**

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#### Question 1: How to Find the Radius of a Circle with the help of a Chord?

Answer: When the chord of the circle is given, including details like length and height, you can easily find its radius. You have to multiply the length of the chord by 4. Suppose the chord is five cm and hence ti find the radius multiply it with four. Like four times five is 20 cm.

#### Question 2: Is the Diameter of the Circle a Chord?

Answer: When both the endpoints of the line segment lie on the circle, the line segment is called the chord of the circle. In the same way, when a chord crosses the circle’s center, it becomes the circle’s diameter.

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