Flashcards · Maths · Circle Theorems
Angles at the Centre and in a Semicircle
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What is a chord?
A straight line joining two points on a circle.
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What is a tangent?
A straight line that touches a circle at one point.
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What is an arc?
A part of the circumference of a circle.
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What is the diameter?
A chord that passes through the centre.
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What does the angle at the centre equal?
Twice the angle at the circumference.
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If the angle at the circumference is \(35^\circ\), what is the angle at the centre?
\(70^\circ\).
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If the angle at the centre is \(100^\circ\), what is the angle at the circumference?
\(50^\circ\).
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What is the angle in a semicircle?
\(90^\circ\).
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What must the line be for the semicircle theorem?
A diameter, passing through the centre.
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What is the reason for a \(90^\circ\) angle at the circumference on a diameter?
The angle in a semicircle is \(90^\circ\).
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What kind of triangle do two radii make?
An isosceles triangle.
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What do the other two angles of a right-angled triangle add up to?
\(90^\circ\).
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What are the two marks for in a circle theorem question?
The angle and the reason.
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Where is the angle at the centre drawn from?
The centre of the circle.
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Do both angles have to come from the same chord?
Yes, from the same two points on the circle.
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How many degrees are in a straight line through the centre?
\(180^\circ\).