Inscribed and central angle - problems

  1. Circular pool
    arc_open The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
  2. Pentagon
    5gon_1 Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
  3. Circumferential angle
    uhly Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 5:3:10. Determine the size of the angles of the triangle ΔABC.
  4. 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.
  5. Diagonal in rectangle
    q In that rectangle ABCD is the center of BC point E and point F is center of CD. Prove that the lines AE and AF divide diagonal BD into three equal parts.
  6. Clock face
    center_angle clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
  7. Diagonals
    stvorec_7 Draw a square ABCD whose diagonals have a length of 6 cm
  8. 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.

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