The amphitheater

The amphitheater has the shape of a semicircle, the spectators sit on the perimeter of the semicircle, the stage forms the diameter of the semicircle. Which of the spectators P, Q, R, S, T sees the stage at the greatest viewing angle?

Correct answer:

A =  90 °

Step-by-step explanation:

P=Q=R=S=T=90  A=90=90

We will be pleased if You send us any improvements to this math problem. Thank you!


You need to know the following knowledge to solve this word math problem:

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

Related math problems and questions:

  • Semicircle
    tales-de-mileto In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
  • Wire D
    semicircle_1 Wire length 1 m is bent so that it forms a semicircle circuit (including the diameter). Determine the radius of the semicircle.
  • Complete construction
    thalet Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of legs.
  • Inscribed triangle
    obluk 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.
  • The chord
    Tetiva 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°?
  • Hexagon in circle
    hexagon_3 Calculate the radius of a circle whose length is 10 cm greater than the circumference of a regular hexagon inscribed in this circle.
  • Circle arc
    pizza Circle segment has a circumference of 135.26 dm and 2096.58 dm2 area. Calculate the radius of the circle and size of the central angle.
  • Circumferential angle
    uhly Vertices of the triangle ΔABC lay on the circle and divided into arcs in the ratio 7:8:7. Determine the size of the angles of the triangle ΔABC.
  • Inscribed circle
    vpisana2 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.
  • Circle inscribed
    inscribed345 Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm.
  • Semicircle
    semicircle_2 To a semicircle with diameter 10 cm inscribe square. What is the length of square sides?
  • 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.
  • Inscribed 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.
  • Thales
    circles_1 Calculate the length of the Thales' circle described to the right triangle with hypotenuse 44.2 cm.
  • Construct rhombus
    koso_vpisana Construct rhombus ABCD if given diagonal length | AC | = 8cm, inscribed circle radius r = 1.5cm
  • Circle section
    circle_segment 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
  • Nine-gon
    9gon_1 Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.