TMUA Geometry & Measurement Concepts 5

Question 1

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

Accepted Answer

√13 units

Answer

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?

Accepted Answer

140 cm²

Answer

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?

Accepted Answer

65°

Answer

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?

Accepted Answer

√(h(2R−h))

Answer

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?

Accepted Answer

12 units

Answer

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

(TMUA) Test of Mathematics for University Admission Practice Test

(TMUA) Test of Mathematics for University Admission Practice Test

TMUA Geometry & Measurement Concepts 5