In this chapter, we provide KSEEB SSLC Class 10 Maths Solutions Chapter 6 Constructions Ex 6.2 for English medium students, Which will very helpful for every student in their exams. Students can download the latest KSEEB SSLC Class 10 Maths Solutions Chapter 6 Constructions Ex 6.2 pdf, free KSEEB SSLC Class 10 Maths Solutions Chapter 6 Constructions Ex 6.2 book pdf download. Now you will get step by step solution to each question.

**Karnataka State Syllabus Class 10 Maths Solutions** **Chapter 6 Constructions Ex 6.2**

**In each of the following, give also the justification of the construction :**Question 1.

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Solution:

r = 6 cm,, d = 10 cm., t = ?

Tangent, PQ = PR = 8 cm.

Steps of Construction :

- A circle with radius 6 cm is drawn taking O’ as centre.
- Point P is marked at 10 cm apart from centre of circle.
- With the half of compass mark M which is the mid-point of OP.
- A circle is drawn at M taking radius MO or MP which intersect the given circle at Q and R.
- Now join PQ from P, and Join PR, required tangents are obtained. If measured it is PQ = PR = 8 cm.

Question 2.

Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.

Solution:

Steps of Construction:

- With ‘O’ as centre two circles are constructed with radii 4 cm and 6 cm.
- Draw OM radius for small circle and drawn perpendicular at M which meets the big circle at P and Q.
- Now PQ is the tangent drawn for a small circle.

Tangent PMQ = 9 cm

Verification : In ⊥∆OMP, ∠M = 90°.

∴ OM^{2} + PM^{2} = OP^{2}

(4)^{2} + PM^{2} = (6)^{2}

PM^{2} = (6)^{2} – (4)^{2} = 36 – 16

PM^{2} = 20

∴ PM = 20−−√ = 4.5 cm.

Similarly,

MQ = 4.5 cm.

∴ PQ = PM + MQ = 4.5 + 4.5

∴ PQ = 9 cm.

Question 3.

Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

Solution:

Draw Pw, Px tangents to circle with centre ‘O’ at P.

Draw Qy, Qz tangents to circle with centre ‘O” at Q.

Tantent, OP = OQ = 7 cm.

Steps of Construction :

- Construct a circle with radius 3 cm with centre O’. Draw the diameter AB and on both sides mark P and Q such that OP = OQ = 7 cm.
- Bisect PO, Mark point M and draw circle of radius MO and centre M. It intersects given circle at w and x.

If joined Pw and Px, required tangents are constructed. - Similarly, bisect OQ, mark point N. Draw a circle of radius NO or NQ with centre N, it meets given circle at y and z points. Join Qy and Qz. These are the required tangents.

Question 4.

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.

Solution:

r = 5 cm.

Angle between tangents is 60°.

Steps of Construction :

- A circle is drawn with centre ‘O’ and radius 5 cm. Draw OA and OB radii and ∠AOB = 120°
- Tangents are drawn at A and B and these intersect at P.
- By measurement, ∠APB = 60°.

Angle between tangents PA and PB is 60°.

∵ ∠AOB and ∠APB Supplementary angles.

Question 5.

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

Solution:

Steps of Construction :

- Draw a line segment AB = 8 cm. Draw two circles with radii 4 cm and 3 cm at A and B.
- To construct tangent from centre A to Centre B, it intersects at ‘O’ which is the midpoint of AB.

Draw circle with radius OA, OB at Centre ‘O’, it intersects circle with centre A at C and D and with centre ‘B’ at E and F. - Now join E to A centre and F, required AE and AF tangents are constructed.
- Similarly ‘B’ centre is joined to C and D, BC and BF tangents are constructed.
- AE and AF are tangents drawn from centre ‘A’ to centre ‘B’.

Tangents drawn from centre B to centre A are BC and BD.

Question 6.

Let ABC be a right triangle in which AB= 6 cm, BC = 8 cm and ∠B = 90°. BD is perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

Solution:

AB and AR are tangents drawn for circle with centre P from external point A.

Steps of Construction :

- ⊥∆ ABC is constructed with BC = 8 cm. (base), ∠B = 90°, AB = 6 cm.
- Draw BD ⊥ AC. , Draw perpendicular bisectors of DC and BC, they intersect at P.
- A circle is drawn with centre P through A, B, D, and C.

For this circle AB and AR tangents are constructed from external point A.

Tangent, AB = AR = 6 cm.

Question 7.

Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.

Solution:

Steps of Construction:

- Draw a circle with the help of a circular bangle kept on paper.
- To draw AB and CD chords for this circle which has no centre. Their perpendicular bisectors meet at ‘O’. Now ‘O’ is the centre of the circle.
- Mark point A on the outside of the circle from centre. Join OA. R is the midpoint of OA.
- A circle is drawn with radius RO or RA which intersects the first circle at P and Q. Now join P from A and from A to Q, required two tangents AP and AQ are constructed.

Tangent, AP = Tangent, AQ.

**All Chapter KSEEB Solutions For Class 10 Maths**

—————————————————————————–**All Subject KSEEB Solutions For Class 10**

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