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1 Answer
Roy Ø.
May 10, 2018

Use Pytagoras on the triangle AEC, and show that #90r=150^2+45^2#. Calculate r from this.

Explanation:

I don't think I will do all the math for you, but remember that in a right triangle, #s_1^2+s_2^2=h^2#
where #s_1# and #s_2# are the sides, and h is the hypotenus.

In the right triangle AEC you have
#s_1=AC=150#
#s_2=CE=r-45#
#h=AE=r#

Therefore, from Pytagoras:
#r^2=150^2+(r-45)^2 =150^2 + r^2 - 90r +45^2#
From this it follows that
#90r=150^2+45^2#

From this it should be easy to find your answer, so I'll leave you here.

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