Mathematics Chapter #: Properties of a Circle. Study Mode

Properties of a Circle. Chords of a circle. Angles in a circle. Angles in the opposite segment. Tangents to a circle. Cyclic Quadrilaterals.

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.Properties of a Circle_ Study Mode1

a) The perpendicular from the centre of a circle to a chord bisects the chord.Properties of a Circle_ Study Mode2

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.Properties of a Circle_ Study Mode3

Angle subtended by an arc at the centre of a circle that is twice the angle subtended by the same arc at the circumference.Properties of a Circle_ Study Mode4

b) Angle in a semi-circle.

An angle in a semi-circle is a right angle.Properties of a Circle_ Study Mode5с) Angle in a same segment.

Angles in the same segment of a circle are equal.Properties of a Circle_ Study Mode6


 

3. Angles in the opposite segment.

Properties of a Circle_ Study Mode7

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

  • Lengths of the tangents are equal.
  • Line joining the external point & the centre xxxx the angle between the tangents.

Properties of a Circle_ Study Mode13


 

Cyclic Quadrilaterals.

Properties of a Circle_ Study Mode14

  • The opposite angles of a cyclic quadrilateral add up to 180〫.
  • The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.

 

1. Chords of a Circle.

Properties of a Circle_ Study Mode15


 

2. Angles in a Circle.

Properties of a Circle_ Study Mode16


 

3. Angles in Opposite Segments.Properties of a Circle_ Study Mode18


 

4. Tangents to a Circle.

Properties of a Circle_ Study Mode19

Properties of a Circle_ Study Mode20

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