Perpendicular Bisector and It's Construction

Q.

How many perpendicular bisectors can be drawn for a line segment?

1. $2$

2. $1$

3. $3$

4. $4$

Q.

AB is a line segment. With A and B as centres and any radius greater than half of AB, draw arcs on either side of AB so that they meet at X and Y as shown. Join XY

There are the two statements:
Statement 1: AB is the perpendicular bisector of XY
Statement 2: XY is the perpendicular bisector of AB
Choose the correct option from below.

1. Only Statement 1 is true
2. Only Statement 2 is true
3. None of the above
4. Both the statements are true

Q. How many perpendicular can a triangle can have?

Q. If the perpendicular bisector of line segment MN intersects it at point K, 10.2 cm from N, the length of MN is:

1. 20.4 cm
2. 5.1 cm
3. 10.2 cm
4. 10 cm

Q. If the perpendicular bisector of line segment $AB$ intersects it at point $M$, $6.8cm$ from $A$, then find the length of $AB$. [2 marks]

Q.

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

1. True

2. False

Q. The circumcircle of a triangle passes through

1. One vertex of the triangle
2. Two vertices
   of the triangle
3. Three vertices
   ofthe triangle
4. Will not pass through any vertex

Q. Find the circumcentre of triangle form by the points $(3,2,-5)$, $(-3,8,-5)$, $(-3,2,-5)$

1. $(0,5,5)$
2. $(0,5,-5)$
3. $(0,-5,0)$
4. None of these

Q. The circumcentre of the triangle formed by the lines 3x-y-5=0, x+3y-5=0, x=y is

1. (3, 1)
2. (5/2, 5/2)
3. (5/4, 5/4)
4. (15/8, 15/8)

Q. In a right angled triangle, the point of intersection of perpendicular bisectors of sides is _________.

1. Internal point of a triangle
2. Midpoint of the hypotenuse
3. External point of a triangle
4. Midpoint of the base

Q. The circumcenter of a right-angled triangle is formed

1. Outside the triangle
2. On the hypotenuse ofthe right triangle
3. Inside the triangle
4. At the midpoint ofthe hypotenuse

Q. The circumcentre of the triangle with vertices (0, 0), (3, 0) and (0, 4) is ;-

1. $(1,1)$
2. $(2,\frac{3}{2})$
3. $(\frac{3}{2},2)$
4. None of these

Q. If O is the circumcentre and P the orthocentre of $\Delta$ABC, then $\overrightarrow{PA}+\overrightarrow{PB}+\overrightarrow{PC}=?$

1. $\overrightarrow{OP}$
2. $2\overrightarrow{PO}$
3. $3\overrightarrow{PO}$
4. $4\overrightarrow{PO}$

Q. A pole stands vertically, inside a scalene triangular park ABC. If the angle of elevation of the top of the pole from each corner of the park is same, then in $\Delta$ ABC, the foot of the pole is at the?

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

Q. In $\Delta ABC$, M and N are the mid-points of AB and AC respectively. The altitude AP to BC interest MN at O.

Q. The perpendicular bisectors of AB and AC of the triangle ABC meet BC at D If the bisectors meet AB at P and AC at Q then find $\angle BDP+\angle CDQ$

1. ${90}^{\circ }$
2. ${100}^{\circ }$
3. ${80}^{\circ }$
4. ${60}^{\circ }$

Q.

In the below figure if AP=BP, AQ=BQ, then AM=BM?

1. Data insufficient
2. Cannot be determined
3. True
4. False

Q. In a triangle ABC with vertices A(1, 2), B(2, 3) and C(3, 1) and $\angle A=co{s}^{-1}\left(\frac{4}{5}\right),\angle B=\angle c=co{s}^{-1}\left(\frac{1}{\sqrt{10}}\right)$ then find the circumcentre of the triangle ABC.

Q.

With A and B as centres and any radius greater than half of AB, draw arcs on either side of AB so that they meet in X and Y as shown. Join XY

These are the two statements:
Statement 1: AB is the perpendicular bisector of XY
Statement 2: XY is the perpendicular bisector of AB
Choose the correct option from below.

1. Only Statement 1 is true

2. Only Statement 2 is true

3. Both the statements are true

4. None of the statements are true

Q. What is incentre.

Q. In $\Delta ABC$, $AB=AC$, and $OB=OC$, choose the correct option.

1. $OA=AB$
2. $OA\perp BC$
3. $OB=OA$
4. None of the above

Q. Show that the origin is the circum-centre of the triangle formed by the vertices (1, 0), (0, -1) and $(\frac{-1}{2},\frac{\sqrt{3}}{2})$.

Q. $\Delta PQR$ is an equilateral triangle an incircle with centre $O$. Find the measure of $\angle POR=$ ?

1. ${60}^{\circ }$
2. ${120}^{\circ }$
3. $(180+60{)}^{\circ }$
4. $(180-120{)}^{\circ }$

Q. Find the circumcentre of a triangle whose vertex are $(0,0),(4,0)$ and $(0,6)$

Q. If the vertices of a triangle are the points with position vectors what are the vectors determined by its sides? Find the length of these vectors.

Q. A ___ bisector divides the line segment into two equal halves and the angles thus formed are both right angles.

1. perpendicular
2. non-perpendicular
3. parallel
4. non-parallel

Q. According to the construction shown in the diagram below, what do we call segment $\overline{CD}$?

1. bisector of $\angle C$
2. median to side $\overline{AB}$
3. altitude to side $\overline{AB}$
4. perpendicular bisector of segment $\overline{AB}$

Q.

With A and B as centres and any radius greater than half of AB, draw arcs on either side of AB so that they meet at X and Y as shown. Join XY. Here XY is the _____

1. perpendicular bisector of AB
2. perpendicular but not the bisector of AB
3. only the bisector of AB
4. perpendicular bisector of AX

Q. Find it :-
if the coordinates of the circumcentre of the triangle formed by the lines $3x-2y=6,3x+4y+12=0$ and $3x-8y+12=0$ is $(\alpha ,\beta )$ then $3\left(\beta -\alpha \right)$equals

Q.

The perpendicular bisector of line segement AB meets AB at O. If AO = 6.5 cm, then AB = _____ cm.

1. 12 cm
2. 13 cm
3. 6.5 cm
4. 10 cm