If PQ, the distance between the center of two circles,
measures 8 units, what is the length of the red curve?
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haasini9
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If PQ, the distance
between the center
of two circles,
measures 8 units,
what is the length of
the red curve?
2
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Correct Question :- If PQ, the distance between the center
of two circles measures 8 units, what is the length of the red curve ? Also given that, angle at centre P and Q is 90° .
Solution :-
we know that,
when two circles touch externally, than, the distance between their centre is equal to sum of their radius .
Than,
Let radius of circle with centre P is x units.
So,
→ radius of circle with centre Q will be = (8 - x) units.
Now, we know that,
Length of arc of circle with radius r and angle at centre θ is = (θ/360°) * 2 * π * r .
Putting all values now , we get :-
→ Length of red curve = Length of arc of circle with centre P + Length of arc of circle with centre Q .
→ Length of red curve = [(90°/360°) * 2 * π * x] + [(90°/360°) * π * (8 - x)]
→ Length of red curve = (1/4)[2π*x + 2π*(8 - x)]
→ Length of red curve = (1/4) * 2π[ x + 8 - x ]
→ Length of red curve = (π/2) * 8
→ Length of red curve = 4 π units. (Ans.)
Hence, Length of red curve will be 4π units.
Step-by-step explanation:
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