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Geometry & Measurement Concepts Flashcards

7 cards from real TMUA 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 Concepts flashcards as text

  1. A circle passes through (0,0), (4,0), and (0,6). What is its radius?

    Answer: √13 units

    The circumcenter lies at (2,3); r = √(4+9) = √13.

  2. In a right prism with a triangular cross-section of area 10 cm² and height 8 cm, all lateral faces are rectangles. If the perimeter of the base is 15 cm, what is the total surface area?

    Answer: 140 cm²

    Total SA = 2·(base area) + (perimeter·height) = 20 + 120 = 140 cm².

  3. The angle between a tangent and a chord drawn from the point of tangency is 65°. What is the inscribed angle subtending the same chord from the other arc?

    Answer: 65°

    By the tangent-chord angle theorem, the angle equals the inscribed angle in the alternate segment, so it is 65°.

  4. A cone is inscribed in a sphere of radius R such that the cone's apex is at the top of the sphere. If the cone's height is h, what is the radius of the cone's base?

    Answer: √(h(2R−h))

    The base circle lies at distance R−h from center; using r² = R²−(R−h)² = 2Rh−h² = h(2R−h).

  5. Two secants from an external point P intersect a circle at A, B and C, D respectively. If PA = 4, PB = 9, PC = 3, what is PD?

    Answer: 12 units

    Power of a point: PA·PB = PC·PD → 4·9 = 3·PD → PD = 12.

  6. A regular tetrahedron has edge length 6 cm. What is its volume?

    Answer: 18√2 cm³

    V = (edge³)/(6√2) = 216/(6√2) = 36/√2 = 18√2 cm³.

  7. The locus of points equidistant from two parallel lines y = 3 and y = −1 is:

    Answer: y = 1

    The midpoint between y = 3 and y = −1 is y = (3+(−1))/2 = 1, which is the locus.