Circumcenter and Construction of Circumcircle in a Triangle

Q.

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

1. 2.9 cm

2. 3.8 cm

3. 2.0 cm

4. 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

1. 40 cm

2. 44 cm

3. 88 cm

4. 30 cm

Q.

In an equilateral triangle ABC, AN ⊥ BC. Prove that AN² = 3BN².

Q.

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

1. an acute-angled

2. an isosceles

3. an obtuse-angled

4. 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 ${45}^{\circ }$ 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?

1. None of these.

2. Construction of a triangle.

3. Construction of perpendicular bisectors.

4. 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, $\angle$ B is ${70}^{\circ }$ and AB-AC=7.

Q.

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

1. $15$

2. $13/2$

3. $15/2$

4. $6$

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.

1. True

2. 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 ${120}^{\circ }$ 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,

1. 6.4 cm, 4.5 cm

2. 3.2 cm, 3 cm

3. 6.4 cm, 7 cm

4. 6.4 cm, 3.5 cm

5. 3.2 cm, 2.5 cm

6. 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 ____

1. 5.5 cm

2. 2.5 cm

3. 3.464 cm

4. 6.4 cm

Q.

In an equilateral triangle ABC, D is point on BC such that BD=1/3BC.Prove that 9AD²=7AB².

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

1. Altitudes
2. Angular Bisectors
3. Perpendicular bisectors
4. Medians

Q. What is incenter?

Q. Construct a triangle in which AB = 4 cm, ∠CAB = ${45}^0$ and BC = 2.92 cm. The side length of AC is:

1. 2.54 cm
2. 3.54 cm
3. 4.54 cm
4. 4.1 cm

Q.

In an equilateral triangle ABC, AN ⊥ BC. Prove that AN² = 3BN².

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?

1. False

2. 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=?

1. 13 cm

2. 7.5 cm

3. 8.5 cm

4. 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.

1. True

2. False

Q.

Construct a triangle BCP given BC=5cm, BP=4cm and $\angle$PBC=45${}^{\circ }$. 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.

1. 5 cm

2. 4.8 cm

3. 6 cm

4. 7 cm

Q.

A Circumcircle passes through the ___ of a polygon