Circumcircle and Its Construction

Q. How to draw a circumcircle?

Q.

Draw an equilateral triangle of side 4.5 cm and draw its circumscribed circle. Find the radius of the circle.

1. 2.6 cm

2. 3.4 cm

3. 2 cm

4. 4 cm

Q.

Construct a triangle ABC in which BC = 4 cm, $\angle ACB={45}^{\circ }$ and perpendicular from A to BC is 2.5 cm. Draw a circle circumscribing the triangle ABC and find its radius.

1. 4 cm

2. 2 cm

3. 3 cm

4. 5 cm

Q. The point of intersection of perpendicular bisectors of a triangle is called .

1. Orthocentre
2. Centroid
3. Circumcentre

Q. Which of the following option does not belong in the construction of circumcircle?

1. Construction of a triangle.
2. Construction of perpendicular bisectors.
3. Construction of circle with radius 2OA. (O is circumcenter and A is one of the vertices of the triangle)
4. None of these.

Q. In a right angled triangle, if base and perpendicular are 5 cm and 12 cm respectively. Find the radius of the circumcircle.

1. $6.5cm$
2. $12cm$
3. $5cm$
4. $7.3cm$

Q. Which of the following option does not belong in the construction of circumcircle?

1. Construction of circle with radius 2OA. (O is circumcenter and A is one of the vertices of the triangle)
2. None of these.
3. Construction of a triangle.
4. Construction of perpendicular bisectors.

Q. Construct $△ABC$ in which $AB=BC=6cm$ and $\angle B={80}^{\circ }$. Locate its incentre and draw the incircle.

Q.

Where does the centre of circumcircle of an obtuse triangle lie?

1. Inside the triangle

2. Outside the triangle

3. On the side of triangle

4. Can't say.

Q.

How many circles can be drawn circumscribing a given triangle?

1. 1

2. infinite

3. 2

4. 3

Q.

Draw a triangle with two sides equal to 5 cm and 6 cm and the angle between them is 45${}^{\circ }$. Then the circumradius of this triangle measures

1. 1.9 cm

2. 2.2 cm

3. 2.8 cm

4. 3.4 cm

Q. Which of the following option does not belong in the construction of circumcircle?

1. Construction of a triangle.
2. None of these.
3. Construction of perpendicular bisectors.
4. Construction of circle with radius 2OA. (O is circumcenter and A is one of the vertices of the triangle)

Q.

Consruct an equilateral triangle ABC of side 5 cm. Draw a circle circumscribing the $△$ABC. Find the length of the circumradius.

1. 2.2 cm

2. 3.8 cm

3. 2.6 cm

4. 4.9 cm

Q. Construct a triangle in which AB = 4 cm, ∠CAB = ${45}^0$ and BC = 2.92 cm. Draw a circle circumscribing the triangle ABC. The radius of the circle is:

1. 2 cm
2. 5 cm
3. 3 cm
4. 4 cm

Q.

The point where the perpendicular bisectors of all three sides of a triangle meet is called

1. the incentre

2. the circumcentre

3. the centroid

4. the orthocentre