The diagram below shows a circle with centre O - Junior Cycle Mathematics - Question 1 - 2018
Question 1
The diagram below shows a circle with centre O.
The five points A, B, C, D, and E are on the circle.
[AB] and [DE] are diameters of the circle, and |∠BOE| = 40°.
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Worked Solution & Example Answer:The diagram below shows a circle with centre O - Junior Cycle Mathematics - Question 1 - 2018
Step 1
Write down the size of the angle X.
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Answer
Since
|∠XOD| = 180°
for diameter [AD], and |∠BOE| = 40°, we can find
|∠X|
using the fact that the angles on a straight line sum up to 180°:
X=180°−40°=140°
Thus,
X = 40°.
Step 2
Work out the size of the angle Y.
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Answer
Triangle AOD is isosceles, so the base angles are equal.
Let |∠AOD| = |∠Y|. Therefore:
180°=40°+2Y
Solving gives:
140°=2YY=2140°=70°
So,
Y = 70°.
Step 3
Work out the size of the angle Z.
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Answer
In cyclic quadrilateral ABCD, opposite angles sum to 180°:
Y+Z=180°Z=180°−70°=110°
Thus,
Z = 110°.
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