Question

If PQ, the distance
between the center
of two circles,
measures 8 units,
what is the length of
the red curve?
​

Answer 1

Answer:

4 π

Step-by-step explanation:

Answer 2

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.