1. Circle Theorem
Remember to look for “basics”
•Angles in a triangle sum to 1800
•Angles on a line sum to 1800
•Isosceles triangles (radius)
•Angles about a point sum to 3600
7. 900
1800
SPECIAL CASE OF THE SAME RULE……… BUT
MAKES A RULE IN ITS OWN RIGHT!!
8. 900
THEOREM 2: Every angle at the circumference
of a SEMICIRCLE, that is subtended by the
diameter of the semi-circle is a right angle.
9. CYCLIC
QUADRILATEARAL
MUST touch the
circumference at
all four vertices
890
1100
700
910
THEOREM 3: Opposite angles sum to 180 in a
cyclic quadrilateral
11. PALE BLUE
AREA IS THE
SEGMENT
RULE 4: Angles at the circumference in the
same SEGMENT of a circle are equal
12. PALE BLUE
AREA IS THE
SEGMENT
RULE 4: Angles at the circumference in the
same SEGMENT of a circle are equal
13. THEOREM 4: Angles at the circumference in
the same SEGMENT of a circle are equal
NOTE: Will lead you to SIMILAR triangles (one
is an enlargement of the other….)
14. • A tangentthe line thatof tangents andone
Enter is a world touches a circle at
point only. This chords….. the point of
point is called
contact.
• A chord is a line that joins two points on the
circumference.
15. Theorem 5 – A tangent is
perpendicular to a radius
900
radius
16. Theorem 6 – Tangents to a circle from
the same point are equal in length
17. Theorem 7 – The line joining an external point to the
centre of a circle bisects the angle between the tangents
350 0
70
350
18. Theorem 5&7 – combined can help you find the missing
angles…..
900
x 350 0
70
y 350
900
19. Theorem 8 – A radius bisects a chord at 900
MIDPOINT
OF THE
CHORD
chord
900
And the chord will be cut perfectly in half!!!
23. Theorem 9 – Alternate angle theorem
The angle between a tangent and a chord
Is equal to the angle in the alternate segment
24. Theorem 9 – Alternate angle theorem
The angle between a tangent and a chord
Is equal to the angle in the alternate segment
25. COMMON EXAM ERROR!
IT TOONLY A
IS IS THINK
DIAMETER
THIS IS A
IF YOU ARE
DIAMETER –
TOLD SO…
SO..
THIS MUST
READ
BE 900 –
QUSETIONS
“TANGENT
CAREFULLY..
MEETS
RADIUS”