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The diagram below shows the centre circle of a soccer pitch - Junior Cycle Mathematics - Question 4 - 2019
Question 4
The diagram below shows the centre circle of a soccer pitch. The centre of the circle is marked. At the start of a game, Gary and the referee stand at two points on ... show full transcript
Worked Solution & Example Answer:The diagram below shows the centre circle of a soccer pitch - Junior Cycle Mathematics - Question 4 - 2019
Step 1
Construct the point J
Answer
- Use a straight edge to draw a line from point G (Gary) through the center of the circle.
- Extend this line until it intersects the circle at a point on the opposite side. Label this point as J.
- Ensure that point J is positioned such that the angle ∠2RG remains at 90°.
Step 2
State a theorem or corollary that justifies your construction in part (a)
Answer
The angle at the center of a circle is twice the angle at any point on the circle standing on the same arc. Therefore, since
, it implies that the angle at the center (which subtends the same arc) will be twice that, or 180° in relation to the straight line construction through points G and J.