# Circles

## Practice Questions:

1. Find the distance between two parallel chords of lengths 14, 48 units of a circle if the radius of the circle is 25 units.

2. Find the radius of the circle if the distance between two parallel chords of length 6 and 8 units is 7 units (drawn on the opposite side of the center).

3. The radius of a circle is 13 cm and the length of one of its chords is 10 cm. Find the distance of the chord from the centre.

4. In the figure given below, O is the centre of the circle. If angle ABO is 40 degrees and angle ACO is 50 degrees, find the measure of angle BOC.

5. In the figure given above, O is the centre of the circle. If angle AOB is 90 degrees and angle AOC is 110 degrees, find the measure of angle BAC,

6. In the figure given below, ACBO is a parallelogram with O as centre of circle. Find the value of angle ACB.

7. In the figure given below, angle DBC is 70 degrees and angle BAC is 40 degrees. Find the measure of angle BCD.

8. In the figure given below, ABC is an isosceles triangle with AB = AC and angle ABC = 50 degrees. Find the measure of the angle BDC and angle BEC.

9. If ABCD is a cyclic trapezium with AD parallel to BC. If angle B is 70 degrees, determine other three angles.

10. ABCD is a cyclic Quadrilateral whose diagonals intersect at a point E. If angle DBC is 70 degrees, Angle BAC = 30 degrees, find angle BCD.

Also if, AB = AC, find the measure of ECD.

11. ABCD is a cyclic trapezium with AB being diameter of the circle. CD is a chord equal to the radius of the circle ans parallel to AB. AD and BC when extended intersect at a point E outside the circle. Find the measure of angle AEB.

1. 31 or 17                        2. 5                              3. 12                                 4. 180                            5. 80                                      6. 120

7. 70                                   8. 80, 100                9. 70, 110, 110            10. 80, 5                       11. 60

# Right Angled Triangles and properties

### Practice Questions:

1. If the greatest side of right-angled triangle is 50 and one side is given as 14, find the third side.

2. If the greatest side of right-angled triangle is 7.5 and one side is given as 6, find the third side.

3.  In a 30-60-90 right angle triangle, the side opposite 90 degrees is given as 20 units, find the remaining two sides.

4.  In a 30-60-90 right angle triangle, the side opposite 60 degrees is given as 30 units, find the remaining two sides.

5.  In a 30-60-90 right angle triangle, the side opposite 30 degrees is given as 15 units, find the remaining two sides.

6. If the length of the side of a square is 50 units, find the length of diagonal.

7. If the length and breadth of rectangle is 60 and 25 units, find the length of diagonal.

8.  In a 45-45-90 right angle triangle, the side opposite 90 degrees is given as 20 units, find the remaining two sides.

9.  In a 45-45-90 right angle triangle, the side opposite 45 degrees is given as 50 units, find the remaining two sides.

10. Find the length of height of equilateral triangle of side 10 units.

11. Find the area of right-angle triangle of dimensions 10, 24 and 26 units.

12. Find the area of an isoscles triangle if the two equal sides are 26 each and one unequal side is 48 units.