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Construct the incircle of the triangle ABC below - Leaving Cert Mathematics - Question a(i) - 2014
Question a(i)
Construct the incircle of the triangle ABC below. Show all your construction lines clearly. **[Figure: Triangle ABC]** (ii) Measure the length of the radius of the... show full transcript
Worked Solution & Example Answer:Construct the incircle of the triangle ABC below - Leaving Cert Mathematics - Question a(i) - 2014
Step 1
Construct the incircle of the triangle ABC
Answer
To construct the incircle of triangle ABC, follow these steps:
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Draw the Triangle: Start by accurately sketching triangle ABC on your paper.
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Locate the Angle Bisectors: Use a compass to bisect each angle of the triangle. To do this for each angle:
- Place the compass point on vertex A, draw an arc that intersects both sides of the angle.
- Without changing the compass width, place the compass on each intersection to draw arcs, creating an intersection point.
- Draw the angle bisector from vertex A through this intersection point.
- Repeat for angles B and C.
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Find the Incenter: The point where all three angle bisectors intersect is the incenter, denoted as point I. Mark this point clearly on your diagram.
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Draw the Incircle: Using a compass, set the width to the distance from point I to any side of the triangle. Draw a circle that touches all three sides of triangle ABC. Ensure that the circle is tangent to each side and clearly show all construction lines.
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Finalization: Label the incenter I and make sure all construction lines and angles are clear.
Step 2
Measure the length of the radius of the circle constructed in part (i)
Answer
To measure the length of the radius of the incircle:
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Use a Ruler: Place a ruler next to the incenter I and measure the distance from I to one of the sides of the triangle (the radius of the incircle).
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Record the Measurement: Ensure your measurement is precise. According to the marking scheme, the length of the radius should be approximately 3 cm.
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Final Answer: Record the measurement as '3 cm' in the provided space.