# Practice Math Challenge Questions for Third Year ( Geometry ) Part 1

Direction: All answers must be exact. Use pi as pi. Time: 1 hour

- The supplement of the complement of an angle is 142°. Find the angle.
- Two sides of a triangle are 10 and 12. How many different triangles can be made out of these sides?
- In parallelogram ABCD, AB//CD, AD//BC. AB=(2x-5) cm, BC= (3x-11) cm, AD= (2x-1) cm. How long is CD?
- ABCD is a cyclic quadrilateral. The measure of angle A is three times the measure of angle C. Find the measure of angle A.
- ABC is right angle at B and inscribed at circle O. AB=3 cm, BC= 4 cm, What is the area of circle O?
- The diagonal of a square measures 4 cm, what is the perimeter of the square?
- The sum of interior angle of a regular polygon is 1260°. How many sides the polygon has?
- What are the maximum points of intersection if we have 6 lines?
- The number of diagonals of a regular polygon is 35. How many sides the polygon has?
- ABCD is a square with an area of 100 cm
^{2}. E is the midpoint of AB. What is the area of triangle DEC? - The surface area of a sphere is 144pi cm
^{2}. What is the volume of the sphere? - The measure of the base angle of an isosceles triangle is twice measure of the vertex angle. What is the measure of the vertex angle?
- Find the area of an equilateral triangle if it altitude is 10 cm?
- Solve for x: 2: 8-x = 4:9
- The ratio of the areas of two similar pentagons is 25:49. If the perimeter of the smaller pentagon is 25 cm, what is the perimeter of the larger pentagon?
- ABCD is a right trapezoid with AB//CD. Angle A=angle D= 90°, angle C= 30°.AB= 6 cm, CD= 10 cm. What is the area of trapezoid?
- ABCD is a square. A smaller square is drawn by connecting the midpoints of the larger square. What is the ratio of the area of smaller square to the larger square?
- A secant PAB is intersects the circle O at A and B such that PA>PB. PT is a tangent line to the same circle such that PT= 2PB, PA=8. How long is PT?
- What is the equation of the line through (2,1) and parallel to 3x-2y-6=0?
- What is the circumference of a circle with an area of 20pi cm?
- In parallelogram ABCD, AC meets BD at O. Suppose OA= 3x-2, OC= 13-6x, OB = 3x+2, find OD.
- The ratio of the angle of quadrilateral is 2:3:4:6. Find the measure of the smallest angle.
- Circles O
_{1}and O_{2}are externally tangent at point P, and have radii 2 cm and 4 cm, respectively. Points A and B, both different from P, are chosen on O_{1}and O_{2}respectively, such that A,P, and B are collinear. If AB=4cm, How long is PB? - Find the volume of a cube with a diagonal of 24 cm.
- Find the area of a circle inscribed in a square with an area of 64 cm
^{2}

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### Dan

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