Circle Geometry Flashcards
Tangent
A line touching a circle/its circumference at one point (that point is called the point of tangency)
Radius
the distance between any point on the circle and the center of the circle. It is equal to half the length of the diameter.
r =
r = C/2TT
r= diameter/ 2
r = area/TT square rooted
Secant
Goes through the circle
Chord
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.
Segment of a chord
The piece of a circle the chord makes and the sector is the section after it
Alternate interior angles
Form a z and are equal
Same side interior angles
Add up to 180 are supplementary
Alternate exterior angles
Equal
Same side exterior angles
Add up to 180
Corresponding angles
Equal
Theorem 1
- The angle at the center of a circle is twice the size of the angle at the circumference.
Theorem 2
- Angles at the circumference in the same segment of a circle and subtended by the same arc/chord are equal.
Theorem 3
- The angle at the circumference that is subtended by the diameter is a right angle
Theorem 4
- The opposite angles of a cyclic quadrilateral are supplementary, they add up to 180 degrees.
A cyclic quadrilateral
A quadrilateral (four sided shape) that has its four vertices/points on the circumference of a circle
Theorem 5
- The EXTERIOR angles of a cyclic quadrilateral is EQUAL TO its/the INTERIOR OPPOSITE ANGLE
Theorem 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
Theorem 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°)
Theorem 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
Theorem 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°)
What is a segment
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
