Bisecting a Line Segment

Q.

Two line segments with common end points form an ________ .

Q.

An arc AB forms $\angle AOB$ at the centre of the circle. If I draw 2 arcs with A and B as centre and a fixed radius 'r' such that they intersect at point P. The line OP will ___________ the $\angle AOB$.

1. be at right angles to

2. bisect

3. trisect

4. be at zero angle to

Q. Perpendicular bisector of any chord of a circle passes through the centre of the circle.

1. False
2. True

Q.

An arc AB forms $\angle AOB$ at the centre of the circle. If I draw 2 arcs with A and B as centre and a fixed radius 'r' such that they intersect at point P. The line OP will __ the $\angle AOB$.

Q. Perpendicular from the centre of a circle to a chord divides the chord in the ratio 2:1.

1. False
2. True

Q.

Step 3: With r as radius, draw arcs with B and C as centres. The point of intersection of the arcs is point D. $\angle DOA$ is__
Note: Answer in degrees.

Q.

An arc AB forms $\angle AOB$ at the centre of the circle. If I draw 2 arcs with A and B as centre and a fixed radius 'r' such that they intersect at point P. The line OP will ___________ the $\angle AOB$.

1. be at right angles to

2. bisect

3. trisect

4. be at zero angle to

Q.

An arc AB forms $\angle AOB$ at the centre of the circle. If we draw 2 arcs with A and B as centre and a fixed radius 'r' such that they intersect at point P. The line OP will ___________ the $\angle AOB$.

1. be at right angles to

2. bisect

3. trisect

4. be at zero angle to

Q.

Given a base angle B and the difference of the sides AC and AB (not necessarily in this order), what is the difference in the steps of constructions when

i) AC $>$ AB

ii) AC $<$ AB

1. Instead of having B as the base angle, have the same construction with C as the base angle

2. Instead of drawing the perpendicular bisector of line segment BC, we’ll draw the angle bisector of angle B in this case

3. Instead of plotting the point D on the ray BX as (AC – AB) = say 2 units, we rewrite it as (AB – AC) = -2 units and plot the point D, 2 units down south of point B on the same ray BX.

4. Instead of having B as the base angle, have the same construction with A as the base angle

Q. If the chord $y=mx+1$ of the circle $x^2+y^2=1$ subtends an angle ${45}^o$ at the major segment of the circle, then value of $m$ is

1. $2$
2. $-2$
3. $-1$
4. None of these

Q. Construct two segments of lengths 4.3 cm and 3.2 cm. Construct a segment whose length is equal to the sum of the lengths of these segments.

Q. The chord of least length which passes through the point $(2,1)$ of the circle $x^2+y^2-2x-4y-13=0$ is

1. $2$
2. $3\sqrt{2}$
3. $2\sqrt{3}$
4. $8$