Cord and Radii

Ans B?

by seeing 3 right angles , we know that there are two squares in this shape.

So let's add up the two sides that are part of the cord on each square:

2(80) + 2(60) = 280


Now we need to include the length of the cord that's actually touching the circle. We can see that each of the two circles only have 3/4 of their circumference touching the cord (because of the right angle excluding 1/4 of the circle from being counted).

So we have :
(3/4)(2(80)Pi + 2(60)Pi) = (3/4)280Pi = 210Pi.


So the answer is 210Pi + 280. B.

My answer is (B) 210pi + 280

Here is the solution:

total length of cord = length of cord(s) between the circles + length of cord surrounding circle 1 + length of cord surrounding circle 2

Length of cord between circles = (80 + 60) + (80 + 60) = 280. [ As you can see its forming squares on both sides).

Length of cord surrounding 1st circle = circumference of circle1 - length of arc not covered

= 2 * pi * 80 - length of arc

Using the formula for length of arc
l = radius * angle covered by arc
l = 80 * pi /2
= 40 * pi

Hence Length of arc surrounding circle1 = 160 * pi - 40 * pi = 120 * pi

Repeat the same to find out for circle2

= 2 * pi * 60 - length of arc
= 120 * pi - 60 * pi/2
= 90 * pi

Add all of them

120pi + 90pi + 280 = 210pi + 280
Ans (B)

Excellent!

OA is indeed B