Family of Circle
Transcript of Family of Circle
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Family Of Circle
By : Murtadha Rafaai (0916063)
Nur Hakimi Bin Mat @ Ahmad ( 0914009)
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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.
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Circle
Circumference
RadiusDiamete
r
Tangent
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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?
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Angles subtended by the same chord are equal
Chord
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Angles subtended by the same chord are equal
The chord is not always drawn in.
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Angles subtended by the same chord are equal
What is the value of a?
a = 35○
35○
a
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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?
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Angle subtended by the same chord at the centre is
twice that at the circumference
2a
a
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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.
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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○
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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?
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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○
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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?
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Angle in a semi circle equal 90○
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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?
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The radius and tangent are at right angles
o
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The radius and tangent are at right angles
o
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The radius and tangent are at right angles
o
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The radius and tangent are at right angles
o
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The radius and tangent are at right angles
o
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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?
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Two tangents from the same point to a circle are
equal