A circular table is shown in the diagram below - Junior Cycle Mathematics - Question 13 - 2014
Question 13
A circular table is shown in the diagram below. Aoife is trying to find the centre of the table.
She constructs the right-angled triangle PQR as shown, with |QR| = 1... show full transcript
Worked Solution & Example Answer:A circular table is shown in the diagram below - Junior Cycle Mathematics - Question 13 - 2014
Step 1
Explain why Aoife is correct.
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Answer
Since |∠PQR| = 90°, this indicates that [PR] is a diameter of the circular table. According to the properties of circles, the center of a circle lies on any diameter. Therefore, the center of the circular table must be along the line segment [PR].
Step 2
Use the Theorem of Pythagoras to calculate the length |PR|.
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Answer
Using the Pythagorean theorem:
∣PR∣2=∣PQ∣2+∣QR∣2
Substituting the known values:
∣PR∣2=(0.75)2+(1)2=0.5625+1=1.5625
Therefore,
∣PR∣=oot1.5625=1.25extm=125extcm.
Step 3
Find the radius of the table.
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Answer
The diameter of the table, |PR|, is 125 cm. The radius is half the diameter, so:
