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. 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.

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 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. "A fuel has calorific value of $25,000kJ/kg$."
What does the above statement represent?

1. $1kg$ of fuel will release $1,00,000kJ$ energy on combustion.
2. $4kg$ of fuel will take $1,00,000kJ$ energy on combustion.
3. $4kg$ of fuel will release $1,00,000kJ$ energy on combustion.
4. $1kg$ of fuel will take $25,000kJ$ energy on combustion.

Q. A gas initially at 0 °C is heated so that its pressure and volume are both doubled. What will be its final temperature?​