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On the diagram below showing the triangle ABC, construct the perpendicular bisector of the side [AC] - Leaving Cert Mathematics - Question 6 - 2021
Question 6
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On the diagram below showing the triangle ABC, construct the perpendicular bisector of the side [AC]. Show all your construction lines and arcs clearly. Construct t... show full transcript
Worked Solution & Example Answer:On the diagram below showing the triangle ABC, construct the perpendicular bisector of the side [AC] - Leaving Cert Mathematics - Question 6 - 2021
Step 1
Construct the perpendicular bisector of the side [AC]
Answer
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Identify Midpoint: Determine the midpoint D of the segment AC. To do this, use a compass to measure the length of AC and mark arcs above and below the line from points A and C.
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Draw Arcs: Keeping the compass width the same, draw arcs above and below the line AC. The intersection of these arcs determines points D1 and D2.
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Draw the Perpendicular Bisector: Use a ruler to draw a straight line through points D1 and D2. This line is the perpendicular bisector of side AC.
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Label the Lines Clearly: Clearly label the midpoint D on the diagram and ensure the perpendicular bisector is marked distinctly.
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Final Checks: Ensure all construction lines and arcs are visible and accurately represent the relationships in the triangle.
Step 2
Construct the circumcircle of the given triangle ABC
Answer
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Identifying the Center: Locate the circumcenter O by drawing the perpendicular bisectors of sides AB and BC. To do this, follow the steps from part (i) for segments AB and BC.
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Draw the Perpendicular Bisectors: For segment AB, find its midpoint and draw the perpendicular bisector using the same technique: find the midpoint and draw arcs above and below.
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Find the Center: The intersection of the perpendicular bisectors will be point O, the circumcenter of triangle ABC.
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Draw the Circumcircle: Using a compass, set the width to the distance from O to any of the triangle's vertices (A, B, or C). Then, draw a circle centered at O that passes through point A, thereby encompassing triangle ABC.
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Label and Finalize: Clearly mark point O as the circumcenter, and ensure that the circle is drawn neatly, signifying the circumcircle construction.