Inscribed and Circumscribed Figures

Inscribed and Circumscribed Figures: Level 4 Challenges


In the right triangle above and altitude is drawn from the right angle to the hypotenuse. Circles are inscribed within each of the smaller triangles.

What is the distance between the centers of these circles?

A chord of a circle divides the circle into two parts such that the squares inscribed in the two parts have areas 16 and 144, respectively.

The radius of the circle is __________.\text{\_\_\_\_\_\_\_\_\_\_}.

The 5 circles have the same size. If the side of the large square is 1, what is the radius of each circle (to 3 decimal places)?

Triangle ABCABC is such that AB=13,BC=14,AB = 13, BC = 14, and CA=15.CA = 15. A point DD on BCBC is placed such that AB+BD=AC+CD.AB + BD = AC + CD. Let XX be the intersection of ADAD with the incircle of ABCABC closest to A.A. Find the length of BX.BX.

Find the value of xx.


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