Line Perpendicular to a Chord from the Center of the Circle

Q. The perpendicular bisector of a chord of a circle always passes through the center.

1. False
2. True

Q.

A circle has only finite number of equal chords. Write True or False. Give reason for your answer

1. True
2. False

Q. The shortest distance between two parallel chords of length 32 units and 24 units of circle having radius 20 units is units

Q. Match the column I with column II for the given image below.

1. ${90}^{\circ }$
2. ${65}^{\circ }$
3. $4$

Q. A circle has a circumference of $20\pi$ units. One of its chord $PQ$ has a length of $12$ units. If $OR\perp PQ,$ then which of the following option is incorrect?

1. radius of the circle is $10$ units
2. $OP=OQ$
3. $PR=6$ units
4. $RQ=5$ units

Q. Equal chords of a circle are located on the same side of the circle's center.

1. True
2. False

Q.

If the radius of the circle is $14\mathrm{cm}$, find its circumference.

Q.

In Figure, if $ \angle ABC=20°$, then $ \angle AOC$ is equal to:

A < 

Q.

Sum of radii of two circles is $140\mathrm{cm}$ and the difference of their circumferences is $88\mathrm{cm}$. Find the diameters of the circles.

Q. Find the area of the right triangle PQY, right-angled at Q, having P as the center of the circle of radius 5 units. The length of the chord ZY is 8 units.
square units

Q. A perpendicular is dropped from the center of a circle to one of its chords. Find the ratio by which the perpendicular divides the chord.

1. $2:1$
2. $4:1$
3. $1:1$
4. $1:3$

Q. The base QY of the given triangle is half of the chord ZY. Also, one of the sides of the triangle passes through the center of the circle. Comment on the type of the triangle.

1. Acute triangle
2. Right triangle
3. Obtuse triangle
4. Scalene triangle

Q. In the figure, if $OC\perp AB,$ then $AC:CB=$

1. $2$
2. $1$
3. $0.5$
4. $3$

Q. In the figure, find $\angle COE?$

1. ${30}^{\circ }$
2. ${60}^{\circ }$
3. ${45}^{\circ }$
4. ${75}^{\circ }$

Q. Two circles of radius 5 units and $\sqrt{45}$ units intersect so that the point of intersections are 6 units apart. The distance between the center of the circles is units.

Q.

What is the locus of the following?

(i) The centre of a wheel of a cycle.

(ii) The door handle as the door opener.

Q.

Two chords $AB$ and $CD$ of a circle are each at distances $4cm$ from the centre. Then $AB=CD$.

Write True or False and justify your answer in each of the following:

1. True
2. False

Q. Find the length of $RS.$ (in cm)

Q. Two chords of equal lengths 5 cm have distances from the center as 3 cm each. Can they be on the same side of the center of the circle?

1. True
2. False