Circumcentre

Q.

In an equilateral triangle, centroid and the circumcentre coincide.

1. True

2. False

Q. Question 1
ABC is a triangle. Locate a point in the interior of $\Delta$ ABC which is equidistant from all the vertices of $\Delta$ ABC.

Q.

Draw a triangle with two sides equal to 4 cm and 5 cm and the angle between them is 60${}^{\circ }$. Then the circumcentre of this triangle lies inside the triangle.

1. False

2. True

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. Draw a triangle with sides equal to 3 cm, 7 cm and 6.5 cm. Then the circumradius of this triangle measures

1. 2.6 cm
2. 2.9 cm
3. 3.1 cm
4. 3.5 cm

Q.

Draw an equilateral triangle of side 5 cm and its circumscribed circle. Find the length of the radius.

1. 3.8 cm

2. 2.9 cm

3. 2.0 cm

4. 4.9 cm

Q.

Draw a triangle with two sides equal to 4 cm and 5 cm and the angle between them is 90${}^{\circ }$. Then the circumcentre of this triangle lies on the third side.

Q. Draw a triangle with sides equal to 3 cm, 7 cm, and 6.5 cm. Also, find it's circumradius.

Q.

Draw a triangle with two sides equal to 4 cm and 5 cm and the angle between them is 120${}^{\circ }$. Then the circumcentre of this triangle lies inside the triangle.

1. True

2. False

Q.

What is the circumradius of a regular hexagon of sides 6 cm?

1. $3\sqrt{2}cm$

2. 3 cm

3. 6 cm

4. $2\sqrt{3}cm$

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

Q. Draw a triangle with two sides of 5 cm and 6 cm and the angle between them is 45${}^{\circ }$. Also, find the circumradius of the triangle measures.

Q. Perpendicular bisectors of a triangle meet at the:

1. Incentre
2. Circumcentre
3. Orthocentre
4. Centroid

Q.

Construct a $\angle$ABC = 60${}^{\circ }$ . Mark a point D on BC such that BD = 6 cm. Find the radius of the circle which touches AB at B and also pass through D.

1. 2.44 cm

2. 4.44 cm

3. 5.48 cm

4. None of these

Q. A/An ____ triangle can be constructed on any given line segment.

Q.

In an equilateral triangle, prove that the centroid and the centre of the circumcircle (circumcentre) coincide. [4 MARKS]