Circumcircle

Q. What is the formula for (A intersection B intersection C) ?

Q. A circle that passes through all the three __________ of a triangle is called as the circumcircle of the triangle.

1. sides
2. vertices
3. altitudes
4. medians

Q. If (A U B)=(A U C) and (A intersection B )=(A intersection C). Then B=C why not A=B=C.??

Q. If U = { a, e, I, o, u} A ={ a, e, i} B = { e, o, u } C= { a, i, u} Then verify that A intersection (B-C ) = ( A intersection B ) - ( A intersection C ) .explain in statement form not in Venn diagram

Q.

The incentre of a triangle is equidistant from its .

Q.

The centre of an incircle is called incentre, Which of the following is true for an incentre ?

1. It is equidistant from the sides of the triangle.

2. It is equidistant from the vertices of the triangle.

3. It is the point of intersection of the perpendicular bisectors of the sides of the triangle.

4. It is the point of intersection of the angular bisectors of the triangle.

Q.

Question 1 (b)

Name the type of the following triangle:

$\Delta ABC$ with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.

Q.

It is not possible to draw the perpendicular bisector of a line segment using a protractor and a ruler with no markings on it.

1. False

2. True

Q. A circle touching all the vertices of a triangle is known as

1. Incircle
2. Orthocentre
3. Circumcircle
4. Median

Q. Draw an equilateral triangle of side 5 cm. Draw its inscribed circle. Measure the radius of the inscribed circle.

Q. The _______ is the centre of a circle which touches all sides of the triangle.

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

Q. The circumcenter of an acute angled triangle is located inside the triangle. The circumcenter of an obtuse angled triangle is located outside the triangle. Where does the circumcenter of a right angled triangle lie?

1. outside the triangle
2. on the triangle
3. inside the triangle
4. None of the above

Q. The point of concurrency of the perpendicular bisectors of a triangle is known as:

1. incentre
2. circumcentre
3. orthocentre
4. centroid

Q. Construct an equilateral triangle of side $6cm$. Construct the circumcentre of it. Then the measure of radius is :

1. $4\sqrt{3}$
2. $\sqrt{3}$
3. $2\sqrt{3}$
4. $3\sqrt{3}$

Q. Construct a $\Delta ABC$ in which $BC=6$ cm, $\angle A={60}^{\circ }$ and altitude through $A$ is $4.5$ cm. Write the steps of construction.

Q. Draw an equilateral triangle. Find its circuncentre $\left(C\right)$, incentre $\left(1\right)$, centroid $\left(G\right)$ and orthocentre $\left(O\right)$. Write your observation.

Q. Construct isosceles triangle with sides $6cm,6cm,8cm$. Construct circumcircle of it. Then the measure of circumradius is :

1. $3.6$
2. $3$
3. $2.4$
4. $5.4$

Q. What is the name of the point indicated by the green arrow?

1. circumcenter
2. incenter
3. orthocenter
4. incircle

Q. Construct the circumcircle and incircle of an equilateral $\Delta$ XYZ with side $6.5$cm and centre O. Find the ratio of the radii of incircle and circumcircle.

Q. Construct a triangle $ABC$ with $AB=4.2cm,BC=6cm$ and $AC=5cm$.
Construct the circumcircle of the triangle drawn.

Q. If one side of a triangle is 12 cm and the opposite angle is 30 degrees, then the diameter of the circumscribed circle is :

1. 30 cm
2. none of these.
3. 18 cm
4. 24 cm
5. 20 cm

Q. Construct the circumcircle of a triangle $ABC$ in which $AB=3cm,\angle B={78}^o$ and $BC=4.6cm$.

Q. A triangle has vertices $A,B$ and $C$ and the respective opposite sides have lengths $a,b$ and $c$. This triangle is inscribed in a circle of radius $R$. If $b=c=1$ and the altitude from $A$ to side $BC$ has length $\sqrt{\frac{2}{3}}$, then $R$ equals.

1. $\frac{1}{\sqrt{3}}$
2. $\frac{2}{\sqrt{3}}$
3. $\frac{\sqrt{3}}{2}$
4. $\frac{\sqrt{3}}{2\sqrt{2}}$

Q. Construct the centroid of $△ABC$ whose sides are $AB=6cm,BC=7cm$, and $AC=5cm$

Q. The point where the perpendicular bisectors of a triangle meet is called the ________.

1. incircle
2. orthocenter
3. circumcenter
4. incenter

Q.

In the figure , name the points which are

(4) in the triangular region of $∆ABC$

Q. Using ruler and compass only, construct a $\Delta$ABC such that $BC=5$cm and $AB=6.5$cm and $\angle$ABC $={120}^o$. Construct a circum-circle of $\Delta$ABC.

Q. For an acute angled triangle circumcenter lies ______ the triangle.

1. outside
2. inside
3. opposite
4. away

Q. Construct a triangle whose sides are $4$cm, $6$cm and $8$cm. Draw the circumcircle of the triangle.

Q. Which of the following is correct regarding construction of circumcentre of a triangle?

1. The circumcenter is the point of concurrency of the three altitudes of each side from opposite vertex of the triangle.
2. The circumcentre of a triangle is the point in the plane equidistant from the three vertices of the triangle
3. The circumcenter is the point of concurrency of the three perpendicular bisectors of each side of the triangle.
4. None of these