# Circumcenter and Construction of Circumcircle in a Triangle

## Trending Questions

**Q.**

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

2.9 cm

3.8 cm

2.0 cm

4.9 cm

**Q.**

How many excenters does a triangle have?

**Q.**

A wire is bent in the form of a circle of radius 28 cm. It is rebent to form a square. The length of the side of the square will be

40 cm

44 cm

88 cm

30 cm

**Q.**

In an equilateral triangle ABC, AN ⊥ BC. Prove that AN^{2} = 3BN^{2}.

**Q.**

If the circumcenter lies on the exterior of a triangle then the triangle is ______ triangle.

an acute-angled

an isosceles

an obtuse-angled

an equilateral

**Q.**ABCD is a square of side length 4 cm. A semicircle with diameter DC is drawn andtangent to the semicircle from A intersects CB at F. Find the length of EF.

**Q.**

Using ruler and compasses only, draw an equilateral triangle of side 4.5 cm and draw its circumscribed circle. Measure the radius of the circle.

**Q.**

Construct a triangle ABC in which BC is 4 cm, Angle B is 45∘ and AB-AC=1.75 cm.

**Q.**Calculate the other sides of a triangle whose shortest side is 6cm and which is similar to a triangle whose sides are 4cm, 7cm, 8cm

**Q.**

Which of the following option does not belong to the construction of a circumcircle?

None of these.

Construction of a triangle.

Construction of perpendicular bisectors.

Construction of angular bisectors.

**Q.**In triangle ABC P is the mid point of AB &PQ is drawn parallel to BC.IF AP=3.5 AQ=4.5 PQ=6 Then the perimeter of ABC is

**Q.**18. The sides of a right angled triangle are in AP. Show that they are in the ratio 3 : 4 : 5.

**Q.**

Construct a triangle ABC in which BC is 8 cm, ∠ B is 70∘ and AB-AC=7.

**Q.**

The circumradius of the triangle whose sides are $13$, $12$, and $5$ is

$15$

$13/2$

$15/2$

$6$

**Q.**

For the construction of a circumcircle of a triangle, we construct the angle bisector of any two angles of the triangle. State whether the given information is true or false.

True

False

**Q.**three side of a triangle are a , 3a and root3 a. find the measurement of angle opposite to the largest side

**Q.**

Construct a triangle ABC in which BC is 5 cm, Angle B is 120∘ and AB+AC=17cm

**Q.**

In ∆ ABC, AB = 12cm, / B = 58^{o}, the perpendicular from A to BC meets it at D. The bisector of /ABC meets AD at E. Calculate correct to one decimal place,

6.4 cm, 4.5 cm

3.2 cm, 3 cm

6.4 cm, 7 cm

6.4 cm, 3.5 cm

3.2 cm, 2.5 cm

3.2 cm, 1.5 cm

**Q.**

Draw an equilateral triangle of sides 6 centimetres and draw its incircle and circumcircle.

**Q.**

The point where the perpendicular bisectors of a triangle intersect is called as ____

5.5 cm

2.5 cm

3.464 cm

6.4 cm

**Q.**

In an equilateral triangle ABC, D is point on BC such that BD=1/3BC.Prove that 9AD^{2}=7AB^{2}.

**Q.**The circumcenter of any triangle is the intersection point of _______ of the three sides of triangle. Fill in the blank with suitable option.

- Altitudes
- Angular Bisectors
- Perpendicular bisectors
- Medians

**Q.**What is incenter?

**Q.**Construct a triangle in which AB = 4 cm, ∠CAB = 450 and BC = 2.92 cm. The side length of AC is:

- 2.54 cm
- 3.54 cm
- 4.54 cm
- 4.1 cm

**Q.**

In an equilateral triangle ABC, AN ⊥ BC. Prove that AN^{2} = 3BN^{2}.

**Q.**

Pavan says that we can construct a triangle if we know its base, a base angle and sum of other two sides. Is he correct?

False

True

**Q.**

In right triangled ABC right angled at B , a line DE is drawn through the mid point D of AB and parallel to BC.If AB=9 cm, BC=12 cm. AE=?

13 cm

7.5 cm

8.5 cm

10 cm

**Q.**

To construct a triangle given its base, a base angle and the difference of the other two sides, a perpendicular bisector needs to be drawn.

True

False

**Q.**

Construct a triangle BCP given BC=5cm, BP=4cm and ∠PBC=45∘. Complete the rectangle ABCD such that:

(1) P is equidistant from AB and BC

(2) P is equidistant from C and D.

Measure and record the length of AB.

5 cm

4.8 cm

6 cm

7 cm

**Q.**

A Circumcircle passes through the