how do you work out the perimeter of a circle which is in a larger one and a chord is given on the tangent to the smaller circle

The best way to go about a problem like this is to create a diagram of what you are actually trying to figure out. So you are starting with a circle

Then we have a circle inside of this circle and since the size of the smaller circle can change we will give this circle a radiusr.

Now the toughest part is placing the chord. It says that the chord rests on top of the smaller circle so we can place it anywhere.

A theorem in geometry is that if a chord touches the edge of a circle it creates a right angle with the radius of that circle.

Then from here we can use the Pythagorean Theorem to help us find the radius of the big circle. Since the length of the chord is x half of that would be 50 and this would be one of the legs of the right triangle, then the radiusrwould be the length of the other leg of the right triangle. So your equation for the radius R of the larger circle can be figured out using the Pythagorean Theorem and looks like the following equation R²= r²+x². Thus i you know the radius r of the smaller circle you can find the radius R of the larger circles radius you then can use A=pR²o find the area of the larger circle.

Hope this helps.

Thank You

Ruchi

Askiitians Faculty