# In the following, give also the justification of the construction: Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its - Mathematics

MCQ
True or False

To construct a triangle similar to a given ∆ABC with its sides 7/3 of the corresponding sides of ∆ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect to BC. The points B1, B2, ...., B7 are located at equal distances on BX, B3 is joined to C and then a line segment B6C' is drawn parallel to B3C where C' lies on BC produced. Finally, line segment A'C' is drawn parallel to AC.

• True

• False

#### Solution

This statement is False.

Explanation:

Let us try to construct the figure as given in the question.

Steps of construction:

1. Draw a line segment BC.

2. With B and C as centres, draw two arcs of suitable radius intersecting each other at A.

3. Join BA and CA and we get the required triangle ∆ABC.

4. Draw a ray BX from B downwards to make an acute angle ∠CBX.

5. Now, mark seven points B1, B2, B3 …B7 on BX, such that BB1 = B1B2 = B2B3 = B3B4 = B4B5 = B5B6 = B6B7.

6. Join B3C and draw a line B7C’ || B3C from B7 such that it intersects the extended line segment BC at C’.

7. Draw C’A’ ||CA in such a way that it intersects the extended line segment BA at A’.

Then, ∆A’BC’ is the required triangle whose sides are 7/3 of the corresponding sides of ∆ABC.

We have,

Segment B6C’ || B3C. But it is clear in our construction that it is never possible that segment B6C’ || B3C since the similar triangle A’BC’ has its sides 7/3 of the corresponding sides of triangle ABC.

So, B7C’ is parallel to B3C.

Concept: Construction of Tangents to a Circle
Is there an error in this question or solution?

#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 10 Construction
Exercise 10.2 | Q 2 | Page 115
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