Topic 3 Geometrical properties of circle

Question 1

A straight line that passes through the centre of a circle and bisects a chord, is perpendicular to the chord. Is the converse also true?

Answer 1

Yes. A perpendicular to a chord that passes through the centre of a circle bisects the chord.
The abbreviation of perpendicular bisector of chord is the “perpendicular symbol” bisector of chord.

Question 2

Chords that are equal in length are equidistant from the centre of a circle.
Is it true that chords that are equidistant from the centre of a circle are equal in length?

Answer 2

yes

Question 3

What are the three properties of circle and its respective abbreviation that you have learnt in worksheet 2?

Answer 3

1. Angles at centre = 2 x angle at circumference. An angle at the centre of a circle is twice any angle at the circumference subtended by the same arc. Abbreviation: The angle sign at centre = 2 angle at circle with a dot inside and “to the power of” ce
2. Angles in same segment of the circle are equal. Abbreviation: angle sign in same segment
3. Every angle at the circumference subtended by a semicircle is a right angle. Abbreviation: rt. Angle sign in semicircle.

Question 4

What is the abbreviation for this property: a straight line that passes through the centre of a circle and bisects a chord, is perpendicular to the chord.

Answer 4

(perpendicular symbol) bisector of chord

Question 5

What is the abbreviation for equal chord: in a circle, chords of equal length are equidistant from its centre?

Answer 5

The abbreviation is equal chords

Question 6

What is the abbreviation for angle at centre is twice any angle at circumference subtended by the same arc?

Answer 6

Abbreviation: (angle sign) at centre is= 2 (angle sign) at circle with dot inside and ce at the top right of circle with dot

Question 7

What are the 10 geometrical properties of circles?

Answer 7

1. (Perpendicular sign) bisector of chord
2. Equal chords
3. (Angle sign) at centre = 2 (angle sign) at circle with dot with ce
4. (Angle sign + s) in same segment
5. rt. (Angle sign) in semicircle
6. (Angle sign + s) in opp.segments
7. Ext (angle sign) of cyclic quad
8. Tangent (perpendicular sign) radius
9. tangents from ext.pt
10. (Angle sign + s) in alt.segments