The above is the image of the question. The brown, blue, green lines are tangent to the circle and the measure of a side of the square is 10. The question is to find the value of the radius.
My Attempt:
I took O as the centre of the circle and drew radius to the tangent point of each tangent. Then I found the lengths of the lines joining the circumcenter and each vertex of the square. But I didn't find any useful relations among the attempts I tried.
So anyone in this community could help me with this question.
Sorry for the bad writing in the picture.
Thank you!
Best Answer
HINT...let the coordinates of the centre of the circle be $(x,y)$ with the bottom left-hand corner of the square being the origin. Then, considering distances from the origin and from other corners of the square to the centre of the circle, you have: $$x^2+y^2=64+r^2$$ $$x^2+(10-y)^2=9+r^2$$ and $$(10-x)^2+(10-y)^2=49+r^2$$
You can solve these simultaneously to get $x$ and $y$ and hence get $r$.