Circle + triangle - math problems

Number of problems found: 181

Inscribed triangle
To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle.
Triangle in circle
Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
Circle section
Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector and
RT and circles
Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.
Inscribed circle
The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
The chord
The side of the triangle inscribed in a circle is a chord passing through the circle center. What size are the internal angles of a triangle if one of them is 40°?
OK circle
Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17.
Circle described
The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
Perimeter of circle
Calculate the circumference of described circle to the triangle with sides 9,12,15 cm.
Equilateral triangle vs circle
Find the area of an equilateral triangle inscribed in a circle of radius r = 9 cm. What percentage of the circle area does it occupy?
Inscribed circle
Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC.
Annulus from triangle
Calculate the content of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25mm, b = 29mm, c = 36mm
Right triangle
A circle with a radius of 5 cm is described in a right triangle with a 6 cm leg. What is the height at the hypotenuse of this triangle?
Right-angled triangle
Determine the content of a right triangle whose side lengths form successive members of an arithmetic progression and the radius of the circle described by the triangle is 5 cm.
Circle inscribed
Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm.
RT - inscribed circle
In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
Cathethus and the inscribed circle
In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.
Circle and rectangle
A rectangle with sides of 11.7 cm and 175 mm is described by circle. What is its length? Calculate the content area of the circle described by this circle.
Inscribed circle
XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm.
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.