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Draw a pair of tangents to a circle of radius 5 cm which are i

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Draw a pair of tangents to a circle of radius $5 c m$ which are inclined to each other at an angle of $60^{o}$ .

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Draw a pair of tangents to a circle of radius

5 c m

which are inclined to each other at an angle of

60^{o}

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

Lets assume a circle with radius =r

and AP and AQ are two external tangents and

20 = 6 0^{o}

be the angle between them.

therefore

∠ C A P = θ

and

∠ CP A = 9 0^{o}

So in

△ C A P, sin θ = sin (\frac{6 0 ^{o}}{2}) = \frac{CP}{C A}

sin (3 0^{o}) = \frac{5}{C A}

C A = 10 c m

Now lets construct this pair of tangents.

Construct a circle with centre c and radius

= 5 c m

locate a point A, which is

10

cm for C such that

C A = 10 c m

Now locate the midpoint of CA be M so that

CM = M A = 5 c m

Now draw a circle with centre M and radius

= CM = 5 c m

and assume that

this circle intersects the previous circle at points P and Q and join the points P,A and Q,A

So that PA and QA are our desire tangents such that

∠ P A Q = 6 0^{o}

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Question Text	Draw a pair of tangents to a circle of radius $5 c m$ which are inclined to each other at an angle of $60^{o}$ .
Answer Type	Text solution:1
Upvotes	150

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

Text solutionVerified

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Draw a pair of tangents to a circle of radius $5 c m$ which are inclined to each other at an angle of $60^{o}$ .