NCERT Solutions class 10 maths chapter 11

Constructions

NCERT Solutions class 10 maths chapter 11 Exercise 11.2

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.

Answer

NCERT Solution Class 10 Ex 11.2 class 10

Step 1:Draw a circle of radius 6cm

Step 2:Make point outside of circle say 'A' such that AO is 10cm

Step 3:Make a perpendicular bisector of AB .P is mid point of AB

Step 4:P as center ,Draw a circle such that it intersect the previous circle at point B and C

Step 5:Join AB and AC

Step 6:AB and AC are the required tangents.

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.

Answer

Step 1: Draw a circle of radius 6 cm with centre 'O'.

Step 2: Again, 'O' as centre draw a circle of radius 4 cm

Step 3:Make a point P on outer circle such that line PO

Step 4:Draw the perpendicular bisector of line OP and M be the mid point of PO.

Step 5:M as center ,Draw a circle such that it intersect the previous circle at point Q and R

Step 6:Join PQ and PR.

Step 7:PQ and PR are the tangents of circle

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.

Answer

Step 1:Draw a circle of radius 3cm with centre 'R'.

Step 2: Produce a diameter of a circle and extends 7 cm at both end and mark point P and T.

Step 3: Draw the perpendicular bisector of the line PR and RT and Q midpoint of PR and S is midpoint of RT.

Step 4: Q as centre ,Draw a circle intersects the circle at A and C

Step 5:Again S as centre ,Draw a circle intersects the circle at B and D

Step 6: join PA and PC .

Step 7: PA and PC are the tangents.

Step 8: Also TB and TD are 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°

Answer

Step 1:Draw a circle of radius 5 cm with centre as O.

Step 2: Take a point Q on the circle and join OQ.

Step 3: Draw a radius OR, angle of 120° with OQ.

Step 4: At point Q and R draw angle 90.

Step 5: Now both the perpendiculars intersect at point P.

Step 6: PQ and PR are the tangents at an angle of 60°

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.

Answer

Step 1:Draw a line AB = 8 cm.

Step 2:Take A as centre draw a circle of radius 4 cm

Step 3: Similarly B as centre, draw a circle of radius 3 cm

Step 4: Draw the perpendicular bisector of the line AB with M midpoint .

Step 5: M as centre draw a circle with the radius of MA the intersects the circle at the points P, Q, R and S.

Step 6: Now join AR, AS, BP and BQ

Step 7: The tangents are AR, AS, BP and BQ

Question 6

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