Circle Geometry

Question 1

Tangent

Answer 1

A line touching a circle/its circumference at one point (that point is called the point of tangency)

Question 2

Radius

Answer 2

the distance between any point on the circle and the center of the circle. It is equal to half the length of the diameter.

Question 3

r =

Answer 3

r = C/2TT
r= diameter/ 2
r = area/TT square rooted

Question 4

Secant

Answer 4

Goes through the circle

Question 5

Chord

Answer 5

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a secant line.

Question 6

Segment of a chord

Answer 6

The piece of a circle the chord makes and the sector is the section after it

Question 7

Alternate interior angles

Answer 7

Form a z and are equal

Question 8

Same side interior angles

Answer 8

Add up to 180 are supplementary

Question 9

Alternate exterior angles

Answer 9

Equal

Question 10

Same side exterior angles

Answer 10

Add up to 180

Question 11

Corresponding angles

Answer 11

Equal

Question 12

Theorem 1

Answer 12

1. The angle at the center of a circle is twice the size of the angle at the circumference.

Question 13

Theorem 2

Answer 13

2. Angles at the circumference in the same segment of a circle and subtended by the same arc/chord are equal.

Question 14

Theorem 3

Answer 14

3. The angle at the circumference that is subtended by the diameter is a right angle

Question 15

Theorem 4

Answer 15

4. The opposite angles of a cyclic quadrilateral are supplementary, they add up to 180 degrees.

Question 16

A cyclic quadrilateral

Answer 16

A quadrilateral (four sided shape) that has its four vertices/points on the circumference of a circle

Question 17

Theorem 5

Answer 17

5. The EXTERIOR angles of a cyclic quadrilateral is EQUAL TO its/the INTERIOR OPPOSITE ANGLE

Question 18

Theorem 6

Answer 18

6. The angle made between a tangent and a chord at the point of contact is equal to the angle in the alternate/opposite segment

Question 19

Theorem 7

Answer 19

7. A tangent of a circle is perpendicular to the radius/diameter of that circle at the point of contact, forming a right angle (90°)

Question 20

Theorem 8

Answer 20

8. The lengths of two tangents from an external point to the points of contact on a circle have equal lengths

AND FORM AN ISOSCELES TRIANGLE

Question 21

Theorem 9

Answer 21

9. The line joining the centre of a circle to the midpoint of a chord is perpendicular to the chord, forming a right angle (90°)

Question 22

What is a segment

Answer 22

a region bounded by a chord and a corresponding arc lying between the chord’s endpoints.

HENCE, AN ALTERNATE OR OPPOSITE SEGMENT IS THE OTHER SEGMENT/ARC