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If the right triangles in the figure shown are similar triangles, what is the lengthof the shorter leg of the larger triangle?
2. A triangle with side lengths of 5, 12, and 15 centimeters is similar to another triangle.The longest side of the other triangle has length 24 centimeters. What is the perimeter,in centimeters, of the larger triangle?
3. Two triangles are graphed on a coordinate plane. Triangle MNP has vertices M(–4, 2), N(–4, 6), and P(–6, 2). Triangle QRS has vertices Q(–5, –1), R(–5, –5), and S(4, –5). Which of the following statements is true?
4. Triangle CAT is an isosceles triangle with vertices (2, 1), (6, 1), and (4, 7). Triangle DOG is similar to triangle CAT, and two of its vertices are (3, –1) and (5, –1). If the third vertex has a y-coordinate that is less than –1, what are the coordinates of the third vertex?
In the figure above,andare parallel andintersectsat V. What is the length of?
Points A and B lie on circle C as shown. The measure of angle ACB is 120°. If the area of circle C is 81π square units, what is the length of minor arc AB?
8. Circle C (not shown) is drawn on a coordinate plane, centered at the origin. If the point(a, b) lies on the circumference of the circle, what is the radius of the circle in termsof a and b?
In the figure above, O is the center of the circle. If the area of ΔXOY is 25, what is the area of the circle?
Each of the three shaded regions above is a semicircle. If AB = 4, BC = 2AB, and CD = 2BC, what is the area of the entire shaded region?
The semicircle shown has its center at point Q. If the measure of the central angle of the shaded sector is 160 degrees, what is the value of x in radians?
The area of the shaded sector in circle P above is 18π square units. If the measure of angle PQR is 45°, what is the length of chord QR?
13. The center of circle O (not shown) falls on the point where the lineintersects the x-axis on the coordinate plane. The point (3, 8) lies on the circumference of the circle.Which of the following could be the equation for circle O?
The figure above shows the path traced by the hand of a scale as it moves from A to B. What is the area, in square inches, of the region passed over by the scale's hand?
15. If arc AB has a length of 12π and represents three-fourths of the circumference of circle O (not shown), what is the shortest distance between the endpoints of the arc?
16. In the figure above, circle O has a circumference of 12π. If AB = 8, what is BC
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