Properties of Circles

The perpendicular bisector of a chord of a circle passes through the ______ of the circle.

A perpendicular line from the centre of a circle to a chord _______ the chord.

Write down the property which states that equal chords of a circle are equidistant from the centre of the circle.

To find the angle at circumference using the '∠ at centre = 2∠ at circumference' property, what is the condition that both the angle at circumference and the angle at centre must satisfy?

• Both the angles at circumference and the angle at centre have to lie in the same segment.

• Both the angles at circumference and the angle at centre have to be bounded by the same arc.

• Both the angles at circumference and the angle at centre have to lie in the opposite segments.

• Both the angles at circumference and the angle at centre have to be bounded by the same chord.

Find the value of x.

• 80

• 228

• 132

• 66

Find the value of x.

• 29

• 77

• 33

• 74

For angles in the same segment, besides having the two angles at the circumference lying in the same segment, what is the other condition that the two angles at the circumference must satisfy?

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Find the value of x and of y.

• x = 108, y = 35

• x = 108, y = 37

• x = 108, y = 36

• x = 37, y = 108

Find angle y.

• 29°

• 58°

• 90°
• 61°