Maths · Geometry. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
These theorems are about chords and tangents. A line from the centre that meets a chord at 90° cuts the chord into two equal halves. This makes a right-angled triangle with the radius as its longest side, so Pythagoras' theorem gives the missing length. Chords of equal length are the same distance from the centre.
Two tangents drawn from one point outside a circle are equal in length. With the two radii they make a kite that has two right angles.
The alternate segment theorem links a tangent to a chord: the angle between them equals the angle that the chord makes at the circumference on the other side of the chord.
Students use the whole chord in Pythagoras' theorem. The right-angled triangle uses half the chord, so halve the chord first, or double your answer if you are finding the chord.
Answer: 65°
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