Locus of Mid Points of Equal Chords of a Circle

Q. The locus of the mid-points of chords of equal length in a circle is a .

1. circle
2. square
3. rectangle
4. ellipse

Q. Proof for binomial theorem

Q.

Equal chords are equidistant from the center. Prove this. In the Proof, which principle are you making use of :

1. Pythagoras Theorem

2. Sum of Angles in a Triangle = 180^o

3. Area of a Triangle = πr²

4. Similarity

5. Congruency

Q.

If two equal chords in a circle are drawn then they are equidistant from the centre of circle.

1. True

2. False

Q.

Draw a triangle ABC in which AB = 6 cm, BC= 4.5 cm and AC= 5 cm.

Draw and label:

(i) the locus of the centres of all circles which touch AB and AC,

(ii) the locus of the centres of all circles of radius 2 cm which touch AB.

Hence, construct the circle of radius 2 cm which touches AB and AC.

Q. What is expended octate rule, .?

Q.

Ram says that two chords are at equal distance from the centre but the chords are not equal to each other.

1. True

2. False

Q.

Pavan asked Preeti to draw a triangle. He gave following data

1.the base BC

2.a base angle, say $\angle$B

3.The difference of other two sides AB - AC or AC - AB, Assume, AB $>$ AC

She was unable to draw the triangle ABC. So as a hint he gave steps of construction but it was not in correct order. He gave following steps

1.Draw the base BC and at point B make an angle say XBC equal to the given angle.

2.Join DC and draw the perpendicular bisector, say PQ of DC.

3.Cut the line segment BD equal to AB - AC from ray BX.

4.Let it intersect BX at a point A. Join AC

​Arrange the steps in correct order.

1. 1, 3, 2, 4

2. 1, 2, 3, 4

3. 1, 4, 3, 2

4. 1, 4, 2, 3

Q.

Using ruler and compasses only:

i) Construct a $\Delta$ABC in which BC = 6cm, $\angle$ABC = 120${}^{\circ }$ and AB = 3.5 cm.

ii) In the above figure draw a circle with BC as diameter. Find a point P on the circumference of the circle that is equidistant from AB and BC. Measure the $\angle$BCP.

1. 60^°

2. 30^°

3. 45^°

4. 50^°

Q.

Draw a circle with centre O and radius 3.5 cm. Take point P at a distance 5.7 cm from the centre. Draw tangents to the circle from point P.

Q. Draw the tangents to the circle from the point $L$ with radius $2.9cm$. Point ${}^{\prime }{L}^{\prime }$ is at a distance $7.5cm$ from the centre ${}^{\prime }{M}^{\prime }$

Q. Draw a circle of radius 5 cm. Draw a pair of tangents to this circle, which are inclined to each other at an angle of ${60}^{\circ }$ [4 MARKS]

Q.

Ram says that two chords are at equal distance from centre but the chords are not equal to each other. Is the statement stated by him true or false?

1. True

2. False

Q. Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 em and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.