Question 1: A chord of length is drawn in a circle of radius . Calculate its distance from the center of the circle.

Answer:

Let the distance from the center

Therefore

Question 2: A chord of length is drawn at a distance of from the center of a circle. Calculate the radius of the circle.

Answer:

Let the radius

Therefore

Question 3: The radius of a circle is and the length of perpendicular drawn from the center to a chord is . Calculate the length of the chord.

Answer:

Let the length of the chord

Therefore

Therefore the length of the chord

Question 4: A chord of length 24 cm is at a distance of 5 cm from the center of the circle. Find the length of the chord of the same circle which is at a distance of 12 cm from the center.

Answer:

Let the radius

Therefore

Let the length of the chord

Therefore

Therefore the length of the chord

Question 5: In the following figure, is a straight line and is the center of both the circles. If and , find the length of .

Answer:

Therefore

Question 6: is the center of the circle of radius . is any point in the circle such that . is the point travelling along the circumference, is the distance from . What are the least and the greatest values of . What is the position of the points at these values . **[1992]**

Answer:

When is on , the least distance of

When is on extended , the greatest distance of

Question 7: In a circle of radius , two parallel chords of length and are drawn. Find the distance between the chords, if both the chord are:

(i) on the opposite side of the center

(ii) on the same side of the center

Answer:

(i) When the chords are on the opposite side of the triangles

Distance of the larger chord from the center

Distance of the smaller chord from the center

Therefore the distance between the chords

(ii) When the chords are on the same side of the triangles

Distance of the larger chord from the center

Distance of the smaller chord from the center

Therefore the distance between the chords

Question 8: Two parallel chords are drawn in a circle of diameter . The length of one chord is . and the distance between the two chords is . Find the length of another chord.

Answer:

Let the distance of the chord from the center

Therefore

Therefore the distance of the other chord from the center

Therefore the length of the other chord

Question 9: A chord of a circle whose center is , is bisected at by a diameter . Given and , calculate the lengths of (i) (ii) and (iii)

Answer:

Question 10: The figure given below, shows a circle with center in which Diameter bisects the chord at point . If and , find the radius of the circle.

Answer:

Let

Therefore

Therefore Radius