10.3 tangents to a circle
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10.3 Tangents to a Circle
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10.3 Tangents to a Circle
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Tangent LineA line that touches a circle at exactly one point
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Point of TangencyThe point where the line touches the circle is called the point of tangency
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Properties of Tangents
Tangent to a Circle
A tangent to a circle is perpendicular to the radius at the point of tangency.
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Properties of TangentsTangent Chord Relationship
A chord drawn perpendicular to a tangent at the point of tangency contains the centre of the circle, and is a diameter.
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D
O
B
F
E
A
Example
a.) What is the measure of ∠BCD?
b.) What is the measure of the central angle ∠DOE?
c.) What type of triangle is △DOE?
D.) What is the measure of ∠DEO?
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ExampleOB = OC, OA = 6, angle C = 30°
Segment AO is parallel to segment BC
Find all mising angles.
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ExampleThe circle has a radius of 3 cm.
AB is tangent to the circle at C.
OA = OB = 5 cm
Find the area of triangle ABO.
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Questions page 3993, 4, 5, 9, 10
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