Square and circles

Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles.

Result

r =  30.5 mm
R =  43.13 mm

Solution:  Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...): Be the first to comment! To solve this example are needed these knowledge from mathematics:

Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

Next similar examples:

1. Concentric circles In the circle with diameter 19 cm is constructed chord 9 cm long. Calculate the radius of a concentric circle that touches this chord.
2. Circle On the circle k with diameter |MN| = 61 J lies point J. Line |MJ|=22. Calculate the length of a segment JN.
3. Base Compute base of an isosceles triangle, with the arm a=20 cm and a height above the base h=10 cm.
4. The chord Calculate a chord length which the distance from the center of the circle (S, 6 cm) equals 3 cm.
5. Chord 5 It is given circle k / S; 5 cm /. Its chord MN is 3 cm away from the center of the circle . Calculate its length.
6. Calculation How much is sum of square root of six and the square root of 225?
7. Oil rig Oil drilling rig is 23 meters height and fix the ropes which ends are 7 meters away from the foot of the tower. How long are these ropes? 8.3 meters long ladder is leaning against the wall of the well, and its lower end is 1.2 meters from this wall. How high from the bottom of a well is the top edge of the ladder? Ladder 6.4 meters long is positioned in the well such that its lower end is distanced from the wall of the well 1.2 m. The upper part of the ladder is supported on the upper edge of the well. How high is the well?
10. Circle annulus There are 2 concentric circles in the figure. Chord of larger circle 10 cm long is tangent to the smaller circle. What are does annulus have?
11. Triangle ABC In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
12. Isosceles IV In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
13. Chord - TS v2 The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
14. Theorem prove We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
15. Center traverse It is true that the middle traverse bisects the triangle? The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart? The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?