Flashcards · Maths · Circle Theorems
The Alternate Segment Theorem
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What is the alternate segment theorem?
The angle between a tangent and a chord equals the angle in the alternate segment.
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Where must the chord start for the theorem to apply?
At the point where the tangent touches the circle.
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What does alternate mean here?
On the other side of the chord.
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Which two lines make the angle between a tangent and a chord?
The tangent and the chord.
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If the tangent-chord angle is \(62^\circ\), what is the angle in the alternate segment?
\(62^\circ\).
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What is a tangent perpendicular to?
The radius at the point of contact.
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What do the angles in a triangle add up to?
\(180^\circ\).
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What are the base angles of an isosceles triangle?
Equal.
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Why is a triangle made by two radii isosceles?
Two of its sides are radii, so they are equal.
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What do you write for the alternate segment theorem?
Angle between tangent and chord equals angle in the alternate segment.
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What should you do first when you see a tangent?
Look for the radius and the chord from the point of contact.
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Can you use the theorem if the chord does not start at the point of contact?
No.
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What do two tangents from one point have in common?
They are equal in length.
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What angle is between a tangent and a diameter at the point of contact?
\(90^\circ\).
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What is the best way to avoid losing marks?
Write the full reason next to every angle.
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How do you check an answer?
Check the angles of each triangle add up to \(180^\circ\).