How can be sure that diameter of the biggest circle is equal to the sum of the diameters of the two small circles?

Hint: The position of the centers of these circles is on the same line

I understood that all three circles have their centers on segment PQ. What does this line and are tangent to point P,R and Q imply?

Tangent means these points touch the circles at just one point. The point being pot P, R and Q right? What does it suggest which is relevant to this q?

Radius could be anywhere on segment PQ right? I still didnt get how are we sure that PR+RQ = PQ ? Are we supposed to rely on the figure provided in the question? I thought we are not supposed to take it on the face vale.

When it says â€śOne circle is tangent to anotherâ€ť, it basically means that the circle is touching the other circle at only one point. Imagine two different-sized circular coins in a cylindrical vessel (say a pringles can). Now try to match all the requirements of the question. The centers of the pringles can, the bigger coin, and the smaller coin should all be on the same line. Also, each coin should touch the other while also touching the edge of the can. Try achieving this in your mind. Hope this helps