Construction of circumcircle and incircle of a triangle
Multiple Choice Questions (MCQ)
- What is the name of the point where two perpendicular bisectors of a triangle intersect?
A. Incentre
B. Centroid
C. Orthocentre
D. Circumcentre
Answer: D. Circumcentre - What is the purpose of drawing angle bisectors in a triangle during incircle construction?
A. To find the centroid
B. To find the circumcentre
C. To find the incentre
D. To find the orthocentre
Answer: C. To find the incentre - Which of the following is true about the incentre of a triangle?
A. It is equidistant from all the vertices
B. It lies outside the triangle
C. It is equidistant from all the sides
D. It lies on one of the sides of the triangle
Answer: C. It is equidistant from all the sides - To draw a circumcircle, what must be done after locating the circumcentre?
A. Draw angle bisectors
B. Measure the side of the triangle
C. Measure the radius from the centre to any vertex
D. Measure the height of the triangle
Answer: C. Measure the radius from the centre to any vertex - The radius of an incircle is measured by:
A. Drawing a median from a vertex
B. Measuring the distance from incentre to a vertex
C. Drawing a perpendicular from incentre to a side
D. Drawing a perpendicular from centroid to a vertex
Answer: C. Drawing a perpendicular from incentre to a side
Short Answer Questions (SAQ)
1.What geometric tool is used to draw the circle once the centre and radius are known?
Answer: A compass.
2.What does the perpendicular bisector of a line segment do?
Answer: It divides the segment into two equal parts at a right angle.
3. Define the circumcentre of a triangle.
Answer: The circumcentre is the point where the perpendicular bisectors of the triangle’s sides intersect.
Long Answer Questions (LAQ)
- Explain the steps to construct the incircle of a triangle with the help of an example.
Answer:
- Draw the triangle ABC.
- Draw angle bisectors of ∠A and ∠B.
- Let the intersection point be P — the incentre.
- From P, draw a perpendicular to side BC and measure its length (say 2 cm).
- Using a compass, draw a circle with centre P and radius 2 cm.
- This circle touches all three sides of the triangle and is the incircle.
- Describe how to construct the circumcircle of a triangle using geometric steps.
Answer:
- Take triangle ABC and choose two sides, say AB and BC.
- Find the midpoints of AB and BC and draw perpendicular bisectors on them.
- Let these bisectors intersect at point O — the circumcentre.
- Measure the distance from O to any vertex, e.g., OA = 6 cm.
- With O as the centre and 6 cm as radius, draw a circle using a compass.
- This circle will pass through A, B, and C — the circumcircle.