Geometry & Measurement Flashcards
7 cards from real AMC 12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Geometry & Measurement flashcards as text
What is the volume of a regular tetrahedron with edge length 6?
Answer: 18√2
V = a³/(6√2) = 216/(6√2) = 18√2.
In triangle ABC, AB = 5, AC = 7, and BC = 8. Point D lies on BC with BD = 3 and DC = 5. What is AD?
Answer: √19
Stewart's theorem: 49·3 + 25·5 = 8(AD² + 15), so AD² = 19.
Two similar triangles have corresponding sides in the ratio 3:5. If the larger triangle has area 50, what is the area of the smaller triangle?
Answer: 18
The areas scale by (3/5)² = 9/25, so the smaller area is 50·9/25 = 18.
Two circles with radii 3 and 5 have centers 10 units apart. What is the length of their common external tangent segment?
Answer: 4√6
sqrt(d² − (r2 − r1)²) = sqrt(100 − 4) = 4√6.
A central angle of a circle measures 140°. What is the measure of an inscribed angle that intercepts the same arc?
Answer: 70°
An inscribed angle is half the central angle that intercepts the same arc.
How many lattice points lie on the circle x² + y² = 25?
Answer: 12
(±5, 0), (0, ±5), (±3, ±4), and (±4, ±3) give 4 + 8 = 12 points.
What is the arc length of a sector with radius 6 and central angle 120°?
Answer: 4π
(120/360)·2π·6 = 4π.
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