Download College Geometry - Sample questions

College Geometry - Sample questions
1. (a) Three sides of a triangle are 5, 6, and 8. Calculate the angles of the
triangle.
(b) Two sides of a triangle are 6 and 9. The angle between them is 30◦ .
Calculate the length of the third side and find the missing angles.
(c) One side of a triangle is 9. The angles at the endpoints of this side
are 30◦ and 45◦ . Calculate the length of the other two sides.
(d) Two sides of a triangle are 8 and 10. The angle opposite to the longer
side is 60◦ . Calculate the length of the third side and find the missing
angles.
2. (a) One side of a triangle is 8. The median corresponding to this side is
10. The height corresponding to this side is 8. Calculate the sides of
the triangle.
(b) The hypotenuse of a right triangle is 10, one of the legs is 5. Find the
length of the other leg and the angles of the triangle. Calculate the
area of the triangle.
(c) The base of an isosceles triangle is 7, the median corresponding to
the base is 9. Calculate the legs and the angles of the triangle.
(d) One side of an isosceles triangle is 10, the medians corresponding to
the other two sides are 12. Calculate the sides and the angles of the
triangle.
3. (a) Three sides of a triangle are 5, 6, and 8. Calculate the radius of the
circumscribed circle and the inscribed circle.
(b) Two sides of a triangle are 6 and 9. The angle between them is 30◦ .
Calculate the radius of the circumscribed circle and the inscribed
circle.
(c) One side of a triangle is 10. The angle next to this side are 45◦ and
60◦ . Calculate the radius of the circumscribed circle and the inscribed
circle.
(d) One side of a triangle is 9. One of the angles next to this side is 60◦ .
The radius of the circumscribe circle is 9. Calculate the sides of the
triangle and the radius of the inscribed circle.
4. (a) The length of the shorter parallel base of a symmetrical trapezoid is
10. The common length of the legs is 5, and the height is 4. Calculate
the area of the trapezoid.
(b) Three side of a symmetrical trapezoid are of length 10, the fourth
side has length 20. Calculate the area of the trapezoid.
(c) In a symmetrical trapezoid the angle of the diagonal and the longer
parallel base is 45◦ , the length of the diagonal is 10. Calculate the
area of the trapezoid.
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(d) The longer diagonal of a rhombus is 12, and one of the angles is 60◦ .
Calculate the sides and the area of the rhombus.
5. (a) Calculate the common length of the sides of a regular decagon inscribed in a circle with radius 4.
(b) The common length of the sides of a regular octagon is 6. Calculate
the area of the octagon.
(c) Let the radius of two circles be 6 and 8. The distance of their centers
is 10. Calculate the distance of the contact points A and B of their
outer common tangent lines.
(d) Let the radius of two circles be 3 and 5. The distance of their centers
is 9. Calculate the distance of the contact points A and B of their
inner common tangent lines.
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