Construction of Circumcircle

Q.

Why do the diagonals of a square intersect at their midpoints $?$

Q. The radius taken to draw the perpendicular bisector for a line segment of length L is

1. L
2. L/4
3. greater than L/3
4. greater than L/2

Q.

ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively interesting at P, Q and R. Then the perimeter of ∆PQR is

1. 1/2 the perimeter of ∆ABC

2. 1/4 the perimeter of ∆ABC

3. 1/3 the perimeter of ∆ABC

4. Twice the perimeter of ∆ABC

Q.

How many arcs are drawn during the construction of a perpendicular bisector?__

Q.

How many arcs are drawn during the construction of a perpendicular bisector?__

Q. Construct a triangle ABC, in which AB = 4 cm, ∠CAB = ${45}^0$ and BC = 2.92 cm. Draw a circle circumscribing the triangle ABC. Find the radius of the circle.
[3 Marks]

Q. In the given figure, how do we obtain the circumcentre?

1. by measuring the height of the triangle
2. by measuring the mid point of one side
3. by drawing perpendicular bisectors of any two sides
4. None of the above

Q. What is the value of AB if BD = 5 cm, AC = 9 cm, and AQ bisects CD perpendicularly?

1. 14 cm
2. 12 cm
3. 4 cm
4. 9 cm

Q. Which of the following options are not steps involved in construction of circumcircle of the $△ABC$ with circumcentre $O$ ?

1. Construction of the given triangle.
2. Construction of perpendicular bisectors of the sides of the triangle.
3. Construction of circle with radius OD (D is the midpoint of BC)
4. Construction of circle with radius $2\times OA$

Q. In $∆$ABC, (fig. 3.75) the perpendicular bisectors of side AB and AC intersect each other at point P. Show that the perpendicular bisector of CB also passes through point P.

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

[3 Marks]

Q. For constructing a perpendicular bisector, the arc radius is more than ____ of the line segment.

1. half
2. one third
3. one fourth
4. one fifth

Q. If a, b and c are the lengths of three sides of a triangle, then which of the following is true?

1. a + b = c
2. a + b < c
3. a - b < c
4. a - b > c

Q. Where circumcentre of a obtuse triangle will be _________.

1. inside of the triangle
2. outside of the triangle
3. on the triangle
4. midpoint

Q. Circumcentre is the concurrent point of perpendicular bisectors of a polygon.

1. True
2. False

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. 3 cm
3. 4 cm
4. 5 cm

Q. For all triangles, ratio of inradius to circumradius is 1:2

1. False
2. True

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

1. Construction of perpendicular bisectors.
2. Construction of a triangle.
3. Construction of circle with radius 2OA. (O is circumcenter and A is one of the vertices of the triangle)
4. Construction of circle with radius 2OA. (O is circumcenter and A is one of the vertices of the triangle)