Pythagorean theorem + circle - practice problems
Number of problems found: 237
- Incircle to circumcircle
Find the ratio of the areas of the incircle and the circumcircle of a square.
- Two circles 3
Two circles are inscribed in a square whose side is 4 cm. Find the radius of the smaller circle.
- Circle inscribed square
What is the area of the circle that can be inscribed in a square of 10 cm?
- A chord 2
A chord of length 16 cm is drawn in a circle of radius 10 cm. Calculate the distance of the chord from the center of the circle.
- ET inscribed circle
An equilateral triangle has been inscribed in a circle with a radius of 4 cm . Find the area of the shaded region.
- Two chords 6
A chord PQ is 10.4cm long, and its distance from the center of a circle is 3.7cm. Calculate the length of a second chord RS, which is 4.1cm from the center of this circle.
- Grassland and goat
An unfenced grassland is a right triangle ABC with AB = 4m, BC = 8m, and AC as hypotenuse. A goat is tied to a 5-m long rope with its stake at point O, which is 2m from side AB and 2m from the prolongation of side BC through corner B. Then: 1. How far is
- Two chords 2
The length of one of two chords of a circle is 12cm. If the chords are 6cm and 7cm, respectively, away from the center of the circle, calculate the length of the second chord.
- Three inscribed objects
A circle is inscribed in a square. An equilateral triangle of side 4√3 is inscribed in that circle. Find the length of the diagonal of the square.
- Find all 2
Find all the complex solutions (write the answer in the form x+iy) of the system. {|z-12|/|z-8i|=5/3 ; |z-4|=|z-8|
- Annular area
The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
- Find radius
Find the radius of the circle using the Pythagorean theorem where a=9, b=r, c= 6+r
- Circle chord
Determine the circle's radius in which the chord 6 cm away from the center is 12 cm longer than the circle's radius.
- Perimeter of circle
Calculate the circumference of a described circle to the triangle with sides 9,12,15 cm.
- Circles
The area of a circle inscribed in a square is 7. What is the area of a circle circumscribed around a square?
- Calculate 2577
Calculate the length of the circle chord, which is 2.5 cm from the circle's center. The radius is 6.5 cm.
- Bridge
The bridge arc has a span of 159 m and a height of 14 m. Calculate the radius of the circle arc of this bridge.
- RT and circles
Solve the right triangle if the radius of the inscribed circle is r=9 and the radius of the circumscribed circle is R=26.
- Circle
The circle k with diameter |MN| = 85. Point J lies on the circle k. Line |NJ|=12. Calculate the length of a segment JM.
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