Name: Tangent to a Circle
Uploaded: 2019-07-19
Duration: 3 min 7 s
Description: Points of intersection are common points between two curves. How many points can be common between a line and a circle? Let's find out through this video.

Question

$∆ ABC ~ ∆ LMN$ . In $∆ ABC, AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm$

Construct $∆ ABC$ and $∆ LMN$ such that $\frac{BC}{MN} = \frac{5}{4}$ .

Accepted Answer

Construct $∆ ABC$ such that $AB = 5.5 cm$ , $BC = 6 cm & CA = 4.5 cm$

$∆ ABC & ∆ LMN$ are similar

Therefore, their corresponding sides are proportional

$\frac{AB}{LM} = \frac{BC}{MN} = \frac{CA}{NL} = \frac{5}{4}$

$\Rightarrow \frac{5.5}{LM} = \frac{6}{MN} = \frac{4.5}{NL} = \frac{5}{4}$

$\Rightarrow LM = \frac{4}{5} \times 5.5 = 4.4 cm, MN = \frac{4}{5} \times 6 = 4.8 cm, NL = \frac{4}{5} \times 4.5 = 3.6 cm$

Now, construct $△ A B C$ and $△ LMN$ .

(i) For $△ A B C$ , first draw $B C = 6 cm$ , then taking $B$ as centre and $5.5 cm$ as the radius draw an arc and taking $C$ as centre and $4.5 cm$ as the radius draw anothera arc which intersects the previous arc at $A$ . Join $A B$ and $A C$ .

(ii) For $△ L M N$ , first draw $M N = 4.8 cm$ , then taking $M$ as centre and $4.4 cm$ as the radius draw an arc and taking $N$ as centre and $3.6 cm$ as the radius draw anothera arc which intersects the previous arc at $L$ . Join $L M$ and $L N$ .

Maharashtra Board Solutions for Chapter: Geometric Constructions, Exercise 1: Practice set 4.1

Maharashtra Board Mathematics Solutions for Exercise - Maharashtra Board Solutions for Chapter: Geometric Constructions, Exercise 1: Practice set 4.1

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