# Inscribed and central angle - examples

1. Circle arc
Circle segment has a circumference of 135.26 dm and 2096.58 dm2 area. Calculate the radius of the circle and size of central angle.
2. Circular pool
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?
3. Pentagon
Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
4. Circumferential angle
Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 2:2:9. Determine the size of the angles of the triangle ΔABC.
5. Complete construction
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.
6. Diagonal in rectangle
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.
7. Clock face
clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
8. Diagonals
Draw a square ABCD whose diagonals have a length of 6 cm
9. Inscribed circle
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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