# Equation + Pythagorean theorem - math problems

#### Number of problems found: 119

- Find radius

Find the radius of the circle using the Pythagorean theorem where a=9, b=r, c= 6+r - Proof PT

Can you easily prove Pythagoras theorem using Euclidean theorems? If so, do it. - Sphere from tree points

Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a - Sphere equation

Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - Equation of circle 2

Find the equation of a circle that touches the axis of y at a distance of 4 from the origin and cuts off an intercept of length 6 on the axis x. - Prove

Prove that k1 and k2 are the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x^{2}+y^{2}+2x+4y+1=0 k2: x^{2}+y^{2}-8x+6y+9=0 - Equation of circle

find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16. - Distance problem 2

A=(x,2x) B=(2x,1) Distance AB=√2, find value of x - Calculate

Calculate the length of a side of the equilateral triangle with an area of 50cm^{2}. - Circle - AG

Find the coordinates of circle and its diameter if its equation is: ? - Circle

The circle touches two parallel lines p and q, and its center lies on line a, which is the secant of lines p and q. Write the equation of the circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0 - Distance problem

A=(x, x) B=(1,4) Distance AB=√5, find x; - Catheti

The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs. - Right

Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ? - On a line

On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1]. - 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]. - Find the 13

Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4]. - Leg and height

Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m. - RT and circles

Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23. - Hyperbola

Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6].

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