Question

1. In ?ABC, let AB = 8, BC = 10, and AC = 9. Suppose the external angle bisector at vertex B intersects line AC at point P. Find PA. 2. Let R and S be points such that RS = 108. The locus of all points, the ratio of whose distances to R and S is 7/5, is a circle. Find the diameter of that circle. 3. In ?ABC, let D and E be points on sides AB and BC, respectively. Suppose DE || AC, and suppose further that ray CD bisects the angle ?ACB. If AC = 28, BC = 21, and BD = 6, find AD, BE, and DE. 4. Let A, B, and C be points on a circle with diameter AB. If BC = 2 and AC = 3, find the radius of the circle. 5. Use the figure. For the named triangle and transversal, write the product of the three ratios equal to -1 by the theorem of Menelaus. (a) ?ABF and transversal E, D, C (b) ?BCD and transversal A, E, F (c) ?EFD and transversal A, B, C (d) ?AEC and transversal F, D, B

          1. In ?ABC, let AB = 8, BC = 10, and AC = 9. Suppose the external angle bisector at vertex B intersects line AC at point P. Find PA.
2. Let R and S be points such that RS = 108. The locus of all points, the ratio of whose distances to R and S is 7/5, is a circle. Find the diameter of that circle.
3. In ?ABC, let D and E be points on sides AB and BC, respectively. Suppose DE || AC, and suppose further that ray CD bisects the angle ?ACB. If AC = 28, BC = 21, and BD = 6, find AD, BE, and DE.
4. Let A, B, and C be points on a circle with diameter AB. If BC = 2 and AC = 3, find the radius of the circle.
5. Use the figure. For the named triangle and transversal, write the product of the three ratios equal to -1 by the theorem of Menelaus.
(a) ?ABF and transversal E, D, C
(b) ?BCD and transversal A, E, F
(c) ?EFD and transversal A, B, C
(d) ?AEC and transversal F, D, B

1. In ?ABC, let AB = 8, BC = 10, and AC = 9. Suppose the external angle bisector at vertex B intersects line AC at point P. Find PA.
2. Let R and S be points such that RS = 108. The locus of all points, the ratio of whose distances to R and S is 7/5, is a circle. Find the diameter of that circle.
3. In ?ABC, let D and E be points on sides AB and BC, respectively. Suppose DE || AC, and suppose further that ray CD bisects the angle ?ACB. If AC = 28, BC = 21, and BD = 6, find AD, BE, and DE.
4. Let A, B, and C be points on a circle with diameter AB. If BC = 2 and AC = 3, find the radius of the circle.
5. Use the figure. For the named triangle and transversal, write the product of the three ratios equal to -1 by the theorem of Menelaus.
(a) ?ABF and transversal E, D, C
(b) ?BCD and transversal A, E, F
(c) ?EFD and transversal A, B, C
(d) ?AEC and transversal F, D, B

Added by Bryan P.

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