Quantitative Aptitude

Geometry

1,950 Questions
All Circle Tangents and Chords 772 Coordinate Geometry 360 Circle and Arc Measures 216 Triangle Centers and Medians 175 Composite and Inscribed Shapes 174 Similarity, Congruence, and Proportionality 118 Right Triangles and Pythagorean Theorem 100 Standard 2D Mensuration 22 Polygon and Angle Sums 10 3D Solid Mensuration 3

Geometry Questions

Multiple choice

Two parallel chords are on one side of the centre of a circle. The length of the two chords is 24 cm and 32 cm. If the distance between the two chords is 8 cm, then what is the area (in cm2) of the circle?

  1. 724.14

  2. 832.86

  3. 924.12

  4. 988.32
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the radius be r and distance from center to chords be x and x+8. Using Pythagoras: r^2 = x^2 + 16^2 and r^2 = (x+8)^2 + 12^2. x^2 + 256 = x^2 + 16x + 64 + 144. 16x = 48 => x = 3. r^2 = 3^2 + 16^2 = 9 + 256 = 265. Area = pi * r^2 = 3.14159 * 265 = 832.52. Option B is the closest.

Multiple choice

Directions: The following question is followed by three statements I, II and III. You have to determine which of the statements is/are necessary/sufficient to answer the question. What is the length of the perpendicular of a right-angled triangle whose perimeter is 30 cm? I. The hypotenuse of the right-angled triangle is 13 cm. II. The sides of the triangle are in ratio 5 : 12 : 13. III. The area of the triangle is 30 cm2.

  1. Only statement I is sufficient.

  2. Only statement II is sufficient.

  3. Only statement III is sufficient.

  4. None of the statements is sufficient to answer the question.

  5. Both statements I and II are sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Two mutually perpendicular chords AB and CD intersect at P. AP = 4 units, PB = 6 units, CP = 3 units. Find the radius of the circle.

  1. 31.251/2 units

  2. 13.251/2 units

  3. 24.251/2 units

  4. 52.251/2 units
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By the intersecting chords theorem, CP x PD = AP x PB, so 3 x PD = 4 x 6 and PD = 8. Using the chord endpoints, the circle has center (1, -5/2), giving radius sqrt(31.25), which is the value represented by option A.

Multiple choice

There is a circle which has a diameter PQ = 34 cm. A chord which is equal to 16 cm, has been drawn from point P to point Y. Find the least distance between centre of circle and the chord of circle.

  1. 15 cm

  2. 16 cm

  3. 17 cm

  4. 18 cm

  5. 19 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The radius of the circle is 34/2 = 17 cm. A chord of 16 cm is drawn. The distance from the center to the chord is the perpendicular bisector, forming a right triangle with the radius as the hypotenuse (17) and half the chord as one leg (8). By Pythagorean theorem, distance^2 + 8^2 = 17^2, so distance^2 = 289 - 64 = 225, distance = 15 cm.