Two circles inscribed in a rectangle

Question:
Given a rectangle with dimensions L=6, H=5. Two circles are inscribed such that they touch each other(circles are adjacent to each other) and also their circumferences touch 2 sides of the rectangle. One of the circles has radius=4. Find the radius of the other circle.

I would really appreciate if you could tell me how to arrive at the answer.

Thank you Amina

Hi Amina,

I think that the circle must have a diameter of 4 units, otherwise it would not fit inside the rectangle. I drew a diagram below with one circle having radius 2 units (diameter 4 units) and the other having an unknown radius of x units.

The right triangle CPD has

|CP| = 5 - 2 - x, |PD| = 6 - 2 - x and |DC| = x + 2 The theorem of Pythagoras implies that |CP|² + |PD|² = |DC|² This gives a quadratic in x which you can solve.

Cheers,
Penny Go to Math Central