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In the given figure, it is known that BD and CE intersect at point A, ED ∥ BC, AB = u, AC = 6.0, AD = 3.0, and the length of AE is equal to 4.5. What is the value of the unknown variable u? | 8.0 |
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In circle O, with diameter AB and chord CD, the line segments AC and AD are connected. If angle BAD measures x degrees, what is the measure of angle ACD? | 63° |
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Given the parallel lines AD, BE, and CF intersecting at A, B, and C, and AB = a units, BC = b units, and DE = d units, compute the length of line EF denoted by 'e' in terms of a, b, and d. | 6 |
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With triangles ABC and DEF being similar as illustrated in the figure, and point O as their center of similarity, what is the ratio of the areas of the two triangles if OE measures 3 times the length of OB? | \frac{1}{9} |
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In the given figure, AD ∥ BE ∥ CF, straight line n and these three parallel lines intersect at points A, B, C and D, E, F respectively. It is known that AB is 20 units long, BC is u units long, DE is 16 units long, and EF is 32 units long. What is the value of the unknown variable u? | 10.0 |
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Given the illustrated diagram where line AB is parallel to line CD, and line AC forms a right angle with line CE at point C, if the measurement of angle BAE is 120°, what is the degree of angle DCE? | 150° |
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Points D and E are respectively on AB and AC of △ABC, and AD: AC = AE: AB = u:20.0. If BC = 60.0, then the length of DE is 30.0. What is the value of the unknown variable u? | 1.0 |
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Xiao Hua measured the height of the building he lived in. He invited his classmates to help and measured that his own shadow length and the shadow length of the building at the same time were 1.0 and u respectively. It is known that Xiao Hua's height is 3.2, so the height of the building where he lives is 96.0. What is the value of the unknown variable u? | 15.0 |
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In the diagram, in triangle ABC, F is the midpoint of BC, and E is a point on side AC, with AC = 50. When the length of AE is () | 25.0 |
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In the given figure, let's denote the height of the overpass as variable h, where h = 10 meters. If the design of the slope satisfies sinA = 1/3, what is the length of the ramp AC, expressed as variable x in terms of h? | 30 |
First 10 examples of xyliu6/geo170k-1k-r1-filtered for development on MLX-VLM.
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