# Circles Exercise 10.2 Solutions – Chapter Circles – Class 10

## Property related to the chords of a circle – Circle

• Equal chords of a circle are equidistant from the centre
• If the chords of a circle are at equal distance from the centre, then they are equal in length
• If the length of the chord increases, its perpendicular distance from the centre decreases.
• If the length of the chord decreases, its perpendicular distance from the centre increases
• The perpendicular distance between the biggest chord and the centre is zero.

## Segment of circle – Circle Exercise 10.2

### Angles in a segment:

• In a circle, an angle in the minor segment is an obtuse angle.
• In a circle, an angle in the major segment is an acute angle.
• An angle in a semi circle is a right angle.
• In a circle, angles in the same segment are equal.

## Circles Exercise 10.2 – Questions:

1. Draw three consecutive circles of radii 1.5 cm, 2.5 cm and 3.5 cm with O as centre.
2. With O1 and O2 as centres draw two circles of same radii 3 cm and with the distance between the two centres equal to 5 cm
3. Draw a line segment AB = 8 cm and mark its midpoint as C. With 2 cm as radius draw three circles having A, B and C as centres. Draw another circle with C as centre and 4 cm radius draw another circle. Identify the name and the concentric circles and congruent circles
4. Draw a circle of radius 4 cm and construct a chord of 6 cm length in it. draw two angles in major segment and two angles in minor segment. Verify that the angles by measuring them.
5. Draw a circle with centre O and radius 3.5 cm and draw a diameter AOB in it. Draw angles in semi- circles on either side of the diameter. Measure the angles and verify that they are right angles.

## Circles Exercise 10.2 – Solutions:

1. Draw three concentric circles of radii 1.5 cm, 2.5 cm and 3.5 cm with O as centre. 2. With O1 and O2 as centres draw two circles of same radii 3 cm and with the distance between the two centres equal to 5 cm

Solution: 3. Draw a line segment AB = 8 cm and mark its midpoint as C. With 2 cm as radius draw three circles having A, B and C as centres. Draw another circle with C as centre and 4 cm radius draw another circle. Identify the name and the concentric circles and congruent circles

Solution: 4. Draw a circle of radius 4 cm and construct a chord of 6 cm length in it. draw two angles in major segment and two angles in minor segment. Verify that the angles by measuring them.

Solution: 5. Draw a circle with centre O and radius 3.5 cm and draw a diameter AOB in it. Draw angles in semi- circles on either side of the diameter. Measure the angles and verify that they are right angles.

Solution: 