Download - Family of Circle
Family Of Circle
By : Murtadha Rafaai (0916063)
Nur Hakimi Bin Mat @ Ahmad ( 0914009)
Aims
• To show the following on a diagram of a circle: radius, diameter, sector, segment, chord and tangent.
• To introduce the circle theorems.• To find unknown angles within a
circle and at tangents to circles using the circle theorems.
Circle
Circumference
RadiusDiamete
r
Tangent
Angles subtended by the same chord
Draw in a chord
Then draw two triangles, using the chord as a base, that touch the circumference.
Measure the angles at the circumference. What do you notice?
Angles subtended by the same chord are equal
Chord
Angles subtended by the same chord are equal
The chord is not always drawn in.
Angles subtended by the same chord are equal
What is the value of a?
a = 35○
35○
a
Angle at the Centre
Draw a triangle with all the vertices touching the circumference.
Draw another triangle using the same base but with a vertex at the centre.Measure the angle at the circumference.Measure the angle at the centre.What do you notice?
Angle subtended by the same chord at the centre is
twice that at the circumference
2a
a
Angle subtended by the same chord at the centre is
twice that at the circumference
2a
a
Sometimes you will have to spot the property being used.
Angle subtended by the same chord at the centre is
twice that at the circumference
25○
What is the value of angle a?
a a50○ 2a = 180○ –
50○
2a = 130○
a = 65○
Cyclic Quadrilaterals
Cyclic Quadrilaterals• Draw a quadrilateral
with all four vertices touching the circumference.
• Measure opposite angles and find their sum.
What do you notice?
The opposite angles of a cyclic quadrilateral add up
to 180○
A cyclic quadrilateral is a quadrilateral whose vertices all lie on the circumference of a circle.
a
b Angle a + angle b = 180○
Angles in a Semi-circle
Draw in a diameter.
Use this as a base to draw a triangle with the vertex at the circumference.
Measure the angle at the circumference.
What do you notice?
Angle in a semi circle equal 90○
Radius and Tangent
Draw in a radius
Draw a tangent meeting the circle at the end of the radius.
Measure the angle between the radius and the tangent.
What do you notice?
The radius and tangent are at right angles
o
The radius and tangent are at right angles
o
The radius and tangent are at right angles
o
The radius and tangent are at right angles
o
The radius and tangent are at right angles
o
Tangents to a Circle
Mark a point outside of the circle.
Draw two tangents to the circle from this point
Measure the lengths of the tangent from the point to the circle.
What do you notice?
Two tangents from the same point to a circle are
equal