# Diameter Radius Circumference of a circle = or Area of a circle = r2r2.

## Presentation on theme: "Diameter Radius Circumference of a circle = or Area of a circle = r2r2."— Presentation transcript:

Circumference of a circle = or

Area of a circle = r2r2

Chord Tangent (minor) Segment (major) Segment

Sector

Angles in the same segment are equal x x x

2a a

Angles held up by the diameter are called “Angles in the semi-circle” and are all 90 0

.. The angle in a semicircle is 90° Isosceles triangles are formed by two radii. Radius Tangent Tangent and Radius meet at 90° 90°. Chord Any chord bisector is a diameter

68 0. c a b = 112 0 opposite angle of a cyclic quadrilateral Opposite angles in cyclic quadrilateral add up to 180 0 (supplementary) Adjacent angles in cyclic trapezium are equal - angles subtended by an arc. Only true if trapezium.

77 0. O a f e c b d Find the missing angles a, b, c, d, e and f 42 0

77 0. O = 42 0 angle in the same segment f e c b d a = 103 0 opposite angle of a cyclic quadrilateral = 103 0 interior angle = 77 0 adjacent angle of a cyclic trapezium 42 0 f = 84 0 angle at the centre is twice the angle at the circumference

... 135 0 87 0 a b. For the following circles, where O is the centre of the circle, find the missing angles. e 48 0 47 0 f g 39 0 110 0 58 0 ik h j 92 0 l m d c o o o o o

... 135 0 87 0 a =93 0 b =45 0. For the following circles, where O is the centre of the circle, find the missing angles. 48 0 47 0 39 0 110 0 58 0 92 0 d = 90 0 c= 90 0 e = 96 0 f = 39 0 31 0 g = 31 0 i=90 0 k=32 0 j=32 0 h=122 0 l=46 0 m=46 0 b c d e f g h a i j k l m o o o o o

m m The angle between chord and tangent The angle in the opposite segment The angle between a chord and a tangent = the angle in the opposite segment n n

always equal in length Two tangents drawn from an outside point are always equal in length, two congruent right-angled triangles so creating an isosceles situation with two congruent right-angled triangles

Two tangents drawn from an outside point are always equal in length, so creating an isosceles situation with two congruent right-angled triangles m m The angle between chord and tangent The angle in the opposite segment The angle between a chord and a tangent = the angle in the opposite segment

A O CE B D 85 0 Find each of the following angles OBE BOD BED BCD CAB 25 0 90 0 170 0 10 0 95 0 25 0 60 0 Angle between tangent and radius is a right angle In kite BEDO, BED = 360-known angles 90 0 + 170 0 + 90 0 =10 0 Opposite angles of a cyclic quad are supplementary The angle between a chord and a tangent = the angle in the opposite segment Angle at the centre is twice the angle at the circumference

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