1.
2.
3.
4.
5.
Period 3:
1. Q: Find, to the nearest tenth, the circumradius and the inradius of a triangle bounded by the lines: y=5x/2-2, y-3=2(x-2)/8, 2x+y=16
A: circumradius=2.8, inradius=1.3
2. Q: A triangle with an area of 48 is inscribed in a circle with area 169π. If two sides of the triangle are 10 and 12, find, to the nearest tenth, the inradius of the triangle.
A: 2.2
3. Q: Find, without doing detailed calculations, the circumradius of a right triangle with a hypotenuse of 17.
A: 8.5
4. Q: In the diagram below, circle O in inscribed in triangle ABC. Triangle DEF is inscribed in circle O. If triangle DEF has the side lengths given, find, to the nearest tenth, the perimeter of triangle ABC. Area of triangle ABC = 128
A: 85.1
5. Q: Consider the diagram below. Circle O is inscribed in triangle ABC. AB = 8 BC = 11 AC = 13 AD = 5 Find, to the nearest tenth, the length of segment OD.
A: 10.4
Period 4
1. Q:
Given: Circle O with inscribed ΔABC, with altitude AD=12 and mA=50°. EA and EB are tangent to Circle O at A and B. mE=36°. Find area of Circle O to the nearest 10th.
A: 170.8
2. Q: Find the difference between the radii of the circumscribed and inscribed circles of a (14, 48, 50) triangle.
A: 19
3. Q: The inscribed circle and circumscribed circle of a given triangle are concentric. Find the ratio between their radii.
A: 1:2
4.
Q: Isosceles ΔABC with leg AB=8 is inscribed inside Circle O as shown. If Circle O has a diameter of 10, find the altitude to a leg to the nearest 10th.
A: 5.8
5.
Q: Given: Rhombus ABCD, with diagonal AC congruent with each of the sides. Circle O is circumscribed around ΔABC, and Circle P is inscribed inside ΔACD. Prove that Point P lies on Circle O.
A:
| Statements | Reasons |
| 1. Given 2. Label midpoint of AC as E 3. ΔABC is congruent to ΔACD 4. ΔABC and ΔACD are equilateral 5. OA~OC~PA~PC 6. OE~PE 7. The incenter, circumcenter, and centroid of an equilateral triangle lie on same point. 8. BO is the perp bis of AC DP is the perp bis of AC 9. BO is parallel to DP 10. BO is collinear to DP 11. BO=radius of circle O, OE=1/2 the radius 12. OE=PE=r/2 13. OP=r 14. P lies on circle O | 1. Given 3. Diagonal of a rhombus divides it into 2 ~ triangles. 4.Definition of a equilateral triangle 5. CPCTC 6.Equidistant from endpoints 7. Concurrence theorems 8. Circumcenter is point of concurrency of the perp bis of sides of triangle. 9. Perpendicular to same segment 10. Parallel and share point E 11. Centroid divides medians in 2:1 ratio 12. Transitive property 13. Addition property 14. Distance to circle O equals radius of circle O. |
Period 5
1. Q: A circle with an area of 60pi is inscribed in a triangle with an area of 55. What is half of the sum of the measures of all the sides?
A: 11(square root(15))/6
2. Q: A triangle with sides 12 and 15 has an area of 54. Find the circumradius.
A: 7.5
3. Q: Two of the sides of a triangle have measures of 3 and 5. If the circumscribed circle has an area of 144pi, what is the altitude to the third side?
A: 1.6
4. Q: A triangle has two sides 13 and 15. If the altitude to the third side is 12, what is the area of the circumscribed circle? (Round to the tenth’s place.)
A: 207.3
5. Q: The ratio of a triangle’s inradius to its circumradius is 2:32. If the triangle’s area is 6 and the product of the measures of the sides if 422, what is the semiperimeter?
A: 1.3