Worksheet 4
1. Two sides of a triangle are 3 cm and 7 cm. The angle between the sides is 40. Calculate
the area of the triangle. How long is the altitude drawn to the side of 7 cm?
2. Two sides of triangle are 8 and 15, its area is 48. How long is the third side? HW
3. The sides of the triangle have lengths
√
a) Determine the angles and the area of the triangle.
b) What is the radius of the circle inscribed into the triangle?
4. The side of square ABCD is 10. Calculate the radius of the circle which passes through
point A, and touches the sides BC and CD.
5. Calculate the radius of the circumscribed circle of a triangle if the sides of the triangle are
15 cm, 9 cm and 12 cm long.
6. The radii of two circles with the same center are 6 cm and 8 cm. What is the distance of
the center from the secant of the circle for which the line segments determined by the
points of intersection with the two circles are 4 cm long?
7. The angle between the tangents to a circle from a point P is 4830’. The radius of the
circle is 10 cm. What is the distance of P from the center of the circle, and what is the
length of the tangent segments?
8. The radius of a circle is 10; the tangent at the point C of the circle has an inclination angle
30 to the chord CB. Otherwise AC is the diameter of the circle. Calculate the area and the
perimeter of the triangle ABC.
9. Let AB be a diameter of a circle of unit radius. Let C be a point of the tangent to the circle
at A for which AC is √ long. Calculate the area of the common part of the triangle
ABC and the circle.*extra HW
10. The area of a triangle is 104 cm2. The lengths of two sides are 15 cm and 20.5 cm. What
are the angle between the two sides, and the length of the altitude drawn to the 20.5 cm
side?
11. In a circle of radius 12 cm determine what arc length and sector area correspond to a
central angle of 80.
12. The central angle of a sector of area 120 cm2 is 67. Determine the radius of the circle.
HW
13. Convert the following angles to radians: 60, 90, 45, 30, 360, 10.
14. Convert the following angles to degree:
15. The central angle on a given arc is
. Determine the corresponding inscribed angle
in degrees and in grad.
16. The area of a sector of a circle is 12 cm2. The radius of the circle is 6 cm. Determine the
central angle of the sector in radians. HW
17. The radius of a circle is 8 cm. What is the area of the two parts of the circle divided by a
√ cm long chord?
18. The radii of two circles are 5 cm. The two points of intersection of the circles are such that
the center of each circle lies on the other circle. Determine the common area of the circle.