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.

Correct answer:

S =  157.5 cm2

Step-by-step explanation:

r=5 y=14 s=(x+y+z)/2 x2=y2+z2 S=sr S=zy/2 zy/2=(z+y+z2+y2)/(2r)  z=2 (y rr2)/(y2 r)=2 (14 552)/(142 5)=452=22.5 x=y2+z2=142+22.52=532=26.5 S=z y/2=22.5 14/2=157.5 cm2

Try calculation via our triangle calculator.




Did you find an error or inaccuracy? Feel free to write us. Thank you!






avatar




Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions:

  • Cathethus and the inscribed circle
    RightTriangleInradius 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.
  • RT - inscribed circle
    rt_incircle 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.
  • Equilateral triangle vs circle
    rs_triangle 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?
  • Pentagon
    5gon Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
  • Inscribed circle
    vpisana The circle inscribed in a triangle has a radius of 3 cm. Express the area of the triangle using a, b, c.
  • Hexagonal pyramid
    hexa_pyramid Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm.
  • 30-gon
    30gon At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
  • Ratio of sides
    described_circle2 Calculate the area of a circle with 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.
  • Right triangle
    rt_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?
  • Hexagon in circle
    hexagon Calculate the radius of a circle whose length is 10 cm greater than the circumference of a regular hexagon inscribed in this circle.
  • 9-gon pyramid
    9gon+Base+cone Calculate the volume and the surface of a nine-sided pyramid, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm.
  • Quarter circle
    quarter_circle What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
  • Inscribed circle
    Cube_with_inscribed_sphere A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base?
  • Nonagon
    9gon Calculate the area and perimeter of a regular nonagon if its radius of the inscribed circle is r = 10cm
  • An equilateral
    rs_triangle2 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?
  • Right triangle eq2
    rt Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
  • Two annuluses
    medzikruzie The area of the annular circle formed by two circles with a common center is 100 cm2. The radius of the outer circle is equal to twice the radius of the inner circle. Determine the outside circle radius in centimeters.