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A chord of a circle is a live segment which has its two end points on the circumference of the circle.

a) The perpendicular from the centre of a circle to a chord bisects the chord.

b) Equal chords of a circle are equivalent from the centre of the circle.

a) Angle at the centre & angle at the circumference.

Angle subtended by an arc at the centre of a circle that is twice the angle subtended by the same arc at the circumference.

b) Angle in a semi-circle.

An angle in a semi-circle is a right angle.с) Angle in a same segment.

Angles in the same segment of a circle are equal.

Sum of angles in the opposite segments of a circle is 180〫.

a) A tangent to a circle is perpendicular to the radius of the circle drawn from the point of contact.

b) Tangents from an external point.

If two tangents are drawn from an external point to a circle, then

1. Chords of a Circle.

2. Angles in a Circle.

3. Angles in Opposite Segments.

4. Tangents to a Circle.

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## 1. Chords of a circle.

A chord of a circle is a live segment which has its two end points on the circumference of the circle.

a) The perpendicular from the centre of a circle to a chord bisects the chord.

b) Equal chords of a circle are equivalent from the centre of the circle.

## 2. Angles in a circle.

a) Angle at the centre & angle at the circumference.Angle subtended by an arc at the centre of a circle that is twice the angle subtended by the same arc at the circumference.

b) Angle in a semi-circle.An angle in a semi-circle is a right angle.

с) Angle in a same segment.Angles in the same segment of a circle are equal.

## 3. Angles in the opposite segment.

Sum of angles in the opposite segments of a circle is 180〫.

## 4. Tangents to a circle.

a) A tangent to a circle is perpendicular to the radius of the circle drawn from the point of contact.b) Tangents from an external point.If two tangents are drawn from an external point to a circle, then

## Cyclic Quadrilaterals.

1. Chords of a Circle.2. Angles in a Circle.3. Angles in Opposite Segments.4. Tangents to a Circle.