TMUA Geometry & Measurement Concepts 5 — Questions and Answers
Question 1: A circle passes through (0,0), (4,0), and (0,6). What is its radius?
- √13 units (Correct answer)
- 2√13 units
- √(52)/2 units
- √7 units
Correct answer: √13 units
The circumcenter lies at (2,3); r = √(4+9) = √13.
Question 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?
- 140 cm² (Correct answer)
- 120 cm²
- 160 cm²
- 100 cm²
Correct answer: 140 cm²
Total SA = 2·(base area) + (perimeter·height) = 20 + 120 = 140 cm².
Question 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?
- 65° (Correct answer)
- 115°
- 130°
- 32.5°
Correct answer: 65°
By the tangent-chord angle theorem, the angle equals the inscribed angle in the alternate segment, so it is 65°.
Question 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?
- √(h(2R−h)) (Correct answer)
- √(2Rh)
- √(Rh)
- √(R²−h²)
Correct 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).
Question 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?
- 12 units (Correct answer)
- 6 units
- 8 units
- 27/4 units
Correct answer: 12 units
Power of a point: PA·PB = PC·PD → 4·9 = 3·PD → PD = 12.
Question 6: A regular tetrahedron has edge length 6 cm. What is its volume?
- 18√2 cm³ (Correct answer)
- 36√2 cm³
- 12√3 cm³
- 9√2 cm³
Correct answer: 18√2 cm³
V = (edge³)/(6√2) = 216/(6√2) = 36/√2 = 18√2 cm³.
Question 7: The locus of points equidistant from two parallel lines y = 3 and y = −1 is:
- y = 1 (Correct answer)
- y = 0
- y = 2
- y = −2
Correct answer: y = 1
The midpoint between y = 3 and y = −1 is y = (3+(−1))/2 = 1, which is the locus.
TMUA Geometry & Measurement Concepts 5
A circle passes through (0,0), (4,0), and (0,6).
What is its radius?