CONSTRUCTIONS: Set B Due Date: February 1, 2013
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1 CNSTRUCTINS: Set B Due Date: February 1, Construct a tangent to a circle at a point on the circle. Given: and point on the circle (see below) Construct: Tangent line on at point P 2. Construct a tangent to a circle from an external point. Given: and an external point Construct: Tangent line to through point P 1
2 3. Construct a common external tangent to two given circles that are not congruent. Given: and (see below) Construct: Common external tangent to and Q 4. Construct a common external tangent to two congruent circles. Given: and (see below) Construct: Common external tangent to and Q 2
3 5. Construct a common internal tangent to two given circles that are not congruent. Given: and (see below) Construct: Common internal tangent to and Q 6. Construct a common internal tangent to two congruent circles. Given: and (see below) Construct: Common internal tangent to and Q 3
4 7. Construct a segment whose length is the geometric mean of the lengths of two given segments. Given: Two segments of given lengths: Construct: Segment whose length is the geometric mean of x and y. x y 8. Given and a line (not intersecting the circle), construct a line that is parallel to line and tangent to. Given: and line l (see below) Construct: Line m tangent to and l 4
5 9. Given and a line (not intersecting the circle), construct a line that is perpendicular to line and tangent to. Given: and line l (see below) Construct: Line m tangent to and l 10. Construct a circle that is circumscribed about a given scalene triangle. Given: Scalene (see below) Construct: Circle circumscribed about C S 5
6 11. Construct a circle that is inscribed in a given right scalene triangle. Given: Right scalene (see below) Construct: Circle inscribed in R G T 12. Construct the orthocenter of an acute scalene triangle. Given: cute scalene (see below) Construct: The orthocenter P of B C 13. Construct the centroid of a scalene obtuse triangle. Given: Scalene obtuse (see below) Construct: The centroid C of B T 6
7 14. Construct a rhombus BCD given its (non-congruent) diagonals and. Given: Diagonals of rhombus BCD: C B D Construct: Rhombus BCD with diagonals and 15. Divide a given segment into five congruent segments. Given: Line segment Construct: Divide (see below) into five congruent segments P Q 16. Construct a circle through three given noncollinear points. Given: Three noncollinear points, B, and C (see below) Construct: The circle through, B, and C B C 7
8 17. Construct a square of given length and construct its circumscribed and inscribed circles. Given: Length of square SQRE Construct: Square SQRE, circumscribed circle about square SQRE and inscribed circle of square SQRE s 18. Construct an inscribed equilateral triangle of given circle. Given: (see below) Construct: Inscribed equilateral of 8
9 19. Construct an inscribed square of a given circle. Given: (see below) Construct: Inscribed square SPNJ of 20. Construct an inscribed hexagon of a given circle. Given: (see below) Construct: Inscribed hexagon HEXGN of 9
10 21. Construct the center of a given circle. Given: Circle (see below) Construct: Center of the circle 22. Construct a rhombus BCD given side and one diagonal. Given: Segments as given B Construct: Rhombus BCD with side and diagonal C 23. Construct an equilateral triangle given the length of an altitude. Given: Segment Construct: Equilateral X with altitude congruent to Y 10
11 24. Given an isosceles trapezoid, construct its circumscribed circle. Given: Isosceles Trapezoid (see below) Construct: Circumscribed circle about trapezoid 25. Given a kite, construct its inscribed circle. Given: Kite (see below) Construct: Inscribed Circle 11
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