Flashcards · Maths · Circle Theorems
Circle Theorem Proofs and Problems
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What does the angle at the centre equal?
Twice the angle at the circumference.
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What makes a triangle isosceles in circle proofs?
Two sides are radii.
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What does the exterior angle of a triangle equal?
The sum of the two opposite interior angles.
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What do the angles of a triangle add up to?
\(180^\circ\).
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What should each line of a proof include?
A reason.
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Why must you not use numbers in a proof?
The proof must work for any angle.
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How do you prove the angle in a semicircle is \(90^\circ\)?
The angle at the centre is \(180^\circ\), so the angle at the circumference is half of it.
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How do you prove opposite angles of a cyclic quadrilateral add up to \(180^\circ\)?
The angles at the centre add up to \(360^\circ\), and each is double.
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What is the gradient of a tangent to a circle at \((a, b)\), centre origin?
\(-\frac{a}{b}\).
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What is the gradient of the radius to \((3, 4)\) from the origin?
\(\frac{4}{3}\).
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What is the gradient of the tangent at \((3, 4)\) on \(x^2 + y^2 = 25\)?
\(-\frac{3}{4}\).
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What formula gives a line through a point?
\(y - y_1 = m(x - x_1)\).
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What do you do first in a multi-step circle problem?
Work out one angle and write its reason.
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Which theorems often combine with the alternate segment theorem?
Triangle angles and isosceles triangles.
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What should you write on the diagram?
Every angle you find.
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Which type of triangle do two radii and a chord make?
Isosceles.