#### SammyS

Staff Emeritus

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Homework Helper

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I will respond for @ehild.as per your approach the value of r= 5.45

i still have a problem with understanding your approach....sorry for bringing this discussion up, i believe its the whole essence of why the forum thrives. Consider the points (3,0) and (0,4), clearly the value of the hypotenuse here, presumably r = 5. Now going with your approach, lets have the same co ordinates, but now (3,r) and (0,4). What value will we get for r? are you implying that,

##3^2+(r-4)^2= r^2##? where

##r=3.125##?

make me understand your way of thoughts...

(Normally, I would be very reluctant to speak for another Helper. - It is perhaps 5:30 am in Hungary as I post this.)

Let's suppose that the question is to find the (length of the) radius of a circle which is tangent to the x-axis at (3,0) and the point (0,4) is also on the circle.

Fantastic! You have found the length of the radius of such a circle to be 3.125 units.

Let's consider some details.

The center of the circle is at (3, 3.125).

The distance of the center from (3, 0) is 3.125.

What is the distance from the center to the point (0,4) ?