# Quadratic equation + right triangle - math problems

- Circle and square

An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD. - An equilateral

An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle? - Two groves

Two groves A, B are separated by a forest, both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B, if AC = 5004 m, BC = 2600 m and angle ABC = 53° 45 ’? - Three parallels

The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle. - A rectangle 2

A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths. - Sides of right angled triangle

One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle. - Secret treasure

Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure. - Medians in right triangle

It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides? - Faces diagonals

If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.3, y=1, z=1.2 - Two chords

Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle. - Touch x-axis

Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis. - Ratio of sides

Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7. - RT sides

Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm. - Perimeter of RT

Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm^{2}. - Find parameters

Find parameters of the circle in the plane - coordinates of center and radius: ? - Rectangle

There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle. - Rectangular triangle

The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle? - Diamond diagonals

Find the diamond diagonal's lengths if the area is 156 cm^{2}and side is 13 cm long. - Diagonals of a rhombus 2

One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm^{2}, find the side of the rhombus. - On line

On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].

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