There's a circle of diameter d that is on a wall, and touches a block. Find the value of d.I'm really unsure how to go about solving this. I wanted to first approach this by using the arc length, but I'm really unsure how to proceed. Anyone have ideas?

Question

There&#039;s a circle of diameter   d that is on a wall, and touches a block. Find the value of   d.I&#039;m really unsure how to go about solving this. I wanted to first approach this by using the arc length, but I&#039;m really unsure how to proceed. Anyone have ideas?

Spielgutq1 · Accepted Answer

If appears that the circle is touching a surface to its left and another surface below it.If we were to graph this circle with these two surfaces representing the x and y axes, the circle would have the equation  (  x  −  r      )    2    +  (  y  −  r      )    2    =      r    2  in order for it to just touch either surface.If the circle also just touches the block that is 5 units wide and 8 units long, the point (5,8) must be on the circle. If we plug this value into the equation, we get  (  5  −  r      )    2    +  (  8  −  r      )    2    =      r    2    25  −  10  r  +      r    2    +  64  −  16  r  +      r    2    =      r    2        r    2    −  26  r  +  89  =  0If we use the quadratic formula, we get solutions of  r  =  13  ±  4      5  One of these solutions,   13  −  4      5  , doesn&#039;t work, though, because the radius becomes too small to leave enough room in the bottom left corner for the block.This means that  r  =  13  +  4      5  which consequently means  d  =  2  r  =  2  (  13  +  4      5    )  =  26  +  8      5

There's a circle of diameter d that is on a wall, and touches a block. Find the value of d.

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