KSEEB SSLC Solutions for Class 10 Maths – Circle – Chord Properties

KSEEB SSLC Solutions for Class 10 Maths – Circle – Chord Properties (English Medium)

Exercise 14.1:

Question 1:

Draw a circle of radius 3.5 cm and construct a chord of length 6 cm in it. Measure the distance between the centre and the chord.

Solution :

Steps of construction:

1. Draw a circle of radius 3.5 cm and centre O.
2. Mark point A on the circle and taking A as the centre and radius equal to 6 cm draw an arc of circle to cut the circle at point B.
3. Join A and B, AB is the required chord of length 6 cm.
4. To measure the distance between the centre and the chord AB, draw OQ ⊥ AB by drawing a perpendicular bisector of AB passing through point O.
5. Measure the length of OQ.

Question 2:

Construct two chords of length 6 cm and 8 cm on the same side of centre of a circle of radius 4.5 cm. Measure the distance between the centre and the chord.

Solution :

Steps of construction:

1. Draw a circle of radius 4.5 cm and centre O.
2. Mark point A on the circle and taking A as the centre and radius equal to 6 cm draw an arc of circle to cut the circle at point B.
3. Join A and B, AB is the required chord of length 6 cm.
4. Mark point C on the circle and taking C as the centre and radius equal to 8 cm draw an arc of circle to cut the circle at point D.
5. Join C and D, CD is the required chord of length 8 cm.
6. To measure the distance between the centre and the chord AB, draw OP ⊥ AB by drawing a perpendicular bisector of AB passing through point O.
7. To measure the distance between the centre and the chord CD, draw OQ ⊥ CD by drawing a perpendicular bisector of CD passing through point O.
8. Measure the length of OQ and OP.
   The length of OQ = 3.35 cm
   the length of OP = 2.06

Question 3:

Construct two chords of length 6.5 cm each on either side of the centre of a circle of radius 4.5 cm. Measure the distance between the centre and the chords.

Solution :

Steps of construction:

1. Draw a circle of radius 4.5 cm and centre O.
2. Mark point A on the circle and taking A as the centre and radius equal to 6.5 cm draw an arc of circle to cut the circle at point B.
3. Join A and B, AB is the required chord of length 6.5 cm.
4. Mark point C on the circle on the other side of the centre and taking C as the centre and radius equal to 6.5 cm draw an arc of circle to cut the circle at point D.
5. Join C and D. AB and CD are the required chords on both the sides of the centre.
6. To measure the distance between the centre and the chord AB, draw OP ⊥ AB by drawing a perpendicular bisector of AB passing through point O.
7. To measure the distance between the centre and the chord CD, draw OQ ⊥ CD by drawing a perpendicular bisector of CD passing through point O.
8. Measure the length of OQ and OP.
   The length of OQ = OP = 3.11 cm

Question 4:

Construct two chords of length 9cm and 7 cm or either side of the centre of a circle of radius 5 cm. Measure the distance between the centre and the chords.

Solution :

Steps of construction:

1. Draw a circle of radius 5 cm and centre O.
2. Mark point A on the circle and taking A as the centre and radius equal to 7 cm draw an arc of circle to cut the circle at point B.
3. Join A and B, AB is the required chord of length 7 cm.
4. Mark point C on the circle on the other side of the centre and taking C as the centre and radius equal to 9 cm draw an arc of circle to cut the circle at point D.
5. Join C and D. AB and CD are the required chords on both the sides of the centre.
6. To measure the distance between the centre and the chord AB, draw OP ⊥ AB by drawing a perpendicular bisector of AB passing through point O.
7. To measure the distance between the centre and the chord CD, draw OQ ⊥ CD by drawing a perpendicular bisector of CD passing through point O.
8. Measure the length of OQ and OP.
   The length of OQ = 2.17 cm, OP = 3.57 cm

Exercise 14.2:

Question 1:

Solution :

	Concentric circle	Congruent circle
Figure 1	C1 and C2	C1 and C3
Figure 2		C1, C2 and C3
Figure 3	C1 and C2 C4 and C5 C6 and C7	C1, C5 and C6 C2, C3, C4 and C7

Question 2:

Draw two concentric circles with centre ‘O’ and radii 2 cm and 3 cm.

Solution :

Steps of construction:

1. Draw a circle of radius OP = 2 cm and centre O.
2. Taking O as the centre and radius OQ = 3 cm, draw another circle.
3. The two concentric circles with centre ‘O’ and radii OP = 2 cm and OQ = 3 cm have been constructed.

Question 3:

Draw three concentric circles of radii 1.5 cm, 2.5 cm and 3.5 cm with O as centre.

Solution :

Steps of construction:

1. Draw a circle of radius OP = 1.5 cm and centre O.
2. Taking O as the centre and radius OQ = 2.5 cm, draw another circle.
3. Again taking O as the centre and radius OR = 3.5 cm, draw one more circle.
4. The three concentric circles with centre ‘O’ and radii OP = 1.5 cm, OQ = 2.5 cm and OR = 3.5 cm have been constructed.

Question 4:

With A and B as centres draw two circles of radii 3.5 cm.

Solution :

Question 5:

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 :

Steps of construction:

1. Draw a line segment O₁O₂ of length 5 cm.
2. Taking O₁ as the centre and radius O₁A = 3 cm, draw a circle.
3. Taking O₂ as the centre and radius = 3 cm, draw another circle.
4. With O₁ and O₂ as centres, two circles of same radii 3 cm and with the distance between the two centres equal to 5 cm are constructed.

Question 6:

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. With C as centre and 4 cm radius draw another circle. Identify and name the concentric circles and congruent circles.

Solution :

Question 7:

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 angles in major segment are acute angles and angles in minor segment are obtuse angles by measuring them

Solution :

Steps of construction:

1. Draw a circle of radius 4 cm and construct a chord of 6 cm length in it.
2. AEPFB is the major segment and ACDB is the minor segment.
3. Construct any two angles ∠AEB and ∠BFA in major segment.
4. Construct any two angles ∠ACB and ∠BDA in minor segment.
5. Angles in major segment are acute angles can be verified by measuring them using protractor.
6. Angles in minor segment are obtuse angles can also be verified by measuring them using protractor.

Question 8:

Draw a circle with centre ‘O’ and radius 3.5 cm and draw 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 :

Steps of construction:

1. Draw a circle with centre ‘O’ and radius 3.5 cm and draw diameter AOB in it.
2. Draw angles in semi-circles on either side of the diameter.
3. Measure the angles using protractor.
4. The angles measure 90°. Hence, it is verified that the angles in semi-circle are right angles.