# RS Aggarwal Solutions Class 10 Chapter 13 Constructions Ex 13B

In this chapter, we provide RS Aggarwal Solutions for Class 10 Chapter 13 Constructions Ex 13B Maths for English medium students, Which will very helpful for every student in their exams. Students can download the latest RS Aggarwal Solutions for Class 10 Chapter 13 Constructions Ex 13B Maths pdf, free RS Aggarwal Solutions Class 10 Chapter 13 Constructions Ex 13B Maths book pdf download. Now you will get step by step solution to each question.

## RS Aggarwal Solutions Class 10 Chapter 13 Constructions Ex 3B

Question 1:

Steps of construction:
Step 1: Draw a circle of radius 5 cm with centre O.
Step 2: A point P at a distance of 8cm from O is taken.
Step 3: A right bisector of OP meeting OP at M is drawn.
Step 4: With centre M radius OM a circle is drawn intersecting the previous circle at T1 and T2
Step 5: Join PT1 and PT2
PT1 and PT2 and the required tangents. Measuring PT1 and PT2
We find, PT1= PT2 =6.2 cm

Question 2:

Steps of construction:
Step 1: Two concentric circles with centre O and radii 4 cm and 6 cm are drawn.
Step 2: A point P is taken on outer circle and O, P are joined.
Step 3: A right bisector of OP is drawn bisecting OP at M.
Step 4: With centre M and radius OM a circle is drawn cutting the inner circle at T1 and T2
Step 5: Join PT1 and PT2
PT1 and PTare the required tangents. Further PT1= PT2 =4.8 cm

Question 3:

Steps of construction:
Step 1: Draw a circle with centre O and radius 3.5 cm
Step 2: the diameter P1P2 is extended to the points A and B such that AO = OB = 7 cm
Step 3: With centre P1 and radius 3.5 cm draw a circle cutting the first circle at T1 and T2
Step 4: join AT1 and AT2
Step 5: With centre P2 and radius 3.5 cm draw another circle cutting the first circle at T3 and T4
Step 6: Join BT3 and BT4 . Thus AT1, AT2 and BT3, BT4 are the required tangents to the given circle from A and B.

Question 4:

Steps of construction:
(i) A circle of radius 4.2 cm at centre O is drawn.
(ii) A diameter AB is drawn.
(iii) With OB as base, an angle BOC of 45° is drawn.
(iv) At A, a line perpendicular to OA is drawn.
(v) At C, a line perpendicular to OC is drawn.
(vi) These lines intersect each other at P.
PA and PC are the required tangents.

Question 5:

Steps of construction:
(i) A line segment AB = 8,5 cm is drawn.
(ii) Draw a right bisector of AB which meets AB at M.
(iii) With M as centre AM as radius a circle is drawn intersecting the given circles at T1, T2, T3 and T4
(iv) Join AT3, ATand BT1, BT2.
Thus AT3, AT4, BT1, BT2 are the required tangents.

Question 6:

Steps of construction:
(i) Draw a line segment AB = 7cm
(ii) Taking A as centre and radius 3 cm, a circle is drawn.
(iii) With centre B and radius 2.5 cm, another circle is drawn.
(iv) With centre A and radius more than 1/2 AB, arcs are drawn on both sides of AB.
(v) With centre B and the same radius, [as in step (iv)] arcs are drawn on both sides of AB intersecting previous arcs at P and Q.
(vi) Join PQ which meets AB at M.
(vii) With centre M and radius AM, a circle is drawn which intersects circle with centre A at T1 and T2 and the circle with centre B at T3 and T4
(viii) Join AT3, AT4, BTand BT2
Thus, AT3, AT4, BT1, BTare the required tangents.

Question 7:

Steps of construction:
(i) A circle of radius 3 cm with centre O is drawn.
(ii) A radius OC is drawn making an angle of 60° with the diameter AB.
(iii) At C, ∠OCP = 90° is drawn.
CP is required tangent.

Question 8:

Steps of construction :
(i) Draw a circle of radius 4 cm with centre O.
(ii) With diameter AB, a line OC is drawn making an angle of 30° i.e., ∠BOC = 30°
(iii) At C a perpendicular to OC is drawn meeting OB at P.
PC is the required tangent.

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