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 maths polygons exterior angles of polygon sum of exterior angles of polygons exterior angles of a polygon

A regular polygon is inscribed in a circle. If a side subtends an angle of $30^{\circ}$ at the centre, what is the number of its sides?

  1. $10$
  2. $8$
  3. $6$
  4. $12$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a polygon of 'n' sides, the angle subtended at the centre is $ \dfrac {{360}^{o}}{n} $

Given, angle at the centre $ = {30}^{o} $
$ => \dfrac {{360}^{o}}{n}= {30}^{o} $
$ => n = 12 $

Hence, the polygon has $ 12 $ sides.

Multiple choice maths pythagoras theorem similarity and right angled triangle angle theorems for a right angled triangle apollonius's theorem

The hypotenuse and the semi-perimeter of right triangle are 20 cm and 24 cm, respectively. The other two sides of the triangle are :

  1. 16 cm, 15 cm

  2. 14 cm, 16 cm

  3. 20 cm, 16 cm

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the sides containing the right angle be a and b, with hypotenuse c = 20 cm. The semi-perimeter is given as 24 cm, meaning the perimeter is 48 cm and a + b + c = 48, so a + b = 28 cm. Using the Pythagorean theorem, a^2 + b^2 = 20^2 = 400. From (a + b)^2 = a^2 + b^2 + 2ab, we get 28^2 = 400 + 2ab, leading to ab = 192. Solving the quadratic equations or checking options, the sides are 12 cm and 16 cm, which are not listed in options A, B, or C. Therefore, None of these is correct.

Multiple choice maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

Given that a right angled trapezium has an inscribed circle. then " the length of the right angled leg is the Harmonic mean of the lengths of bases. "that  statement is __

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a right-angled trapezium with an inscribed circle, the height (the right-angled leg) is indeed the geometric mean of the bases, and the harmonic mean relationship is a known property.

Multiple choice

A circle has a radius of 10 cm. What is the length of a chord that is 8 cm away from the center of the circle?

  1. 6 cm

  2. 8 cm

  3. 10 cm

  4. 12 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The length of a chord that is d units away from the center of a circle with radius r is given by (\sqrt{r^2 - d^2}). If the radius is 10 cm and the chord is 8 cm away from the center, then the length of the chord is 8 cm.

Multiple choice

In a right triangle, if the hypotenuse is 10 and one leg is 6, what is the length of the other leg?

  1. 4

  2. 8

  3. 12

  4. 16
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the Pythagorean theorem, we have $a^2 + b^2 = c^2$. Substituting the given values, we get $6^2 + b^2 = 10^2$. Solving for $b$, we get $b = 8$.

Multiple choice

In a right triangle ABC, the angle B is 30 degrees and the hypotenuse AC is 10 cm. Find the length of the side AB.

  1. 5 cm

  2. 5√3 cm

  3. 10 cm

  4. 10√3 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a right triangle, the sine of an angle is equal to the ratio of the opposite side to the hypotenuse. In this case, sin(B) = AB/AC. Substituting the given values, we get sin(30) = AB/10. Solving for AB, we get AB = 10 * sin(30) = 5√3 cm.

Multiple choice

In a right triangle ABC, the angle C is 45 degrees and the hypotenuse AC is 12 cm. Find the length of the side AB.

  1. 6 cm

  2. 6√2 cm

  3. 8 cm

  4. 8√2 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a right triangle, the cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse. In this case, cos(C) = AB/AC. Substituting the given values, we get cos(45) = AB/12. Solving for AB, we get AB = 12 * cos(45) = 6√2 cm.

Multiple choice

Which theorem states that in a circle, the angle formed by two chords intersecting inside the circle is equal to half the sum of the intercepted arcs?

  1. Pythagorean Theorem

  2. Triangle Inequality Theorem

  3. Angle Sum Theorem

  4. Inscribed Angle Theorem
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Inscribed Angle Theorem states that in a circle, the angle formed by two chords intersecting inside the circle is equal to half the sum of the intercepted arcs.

Multiple choice

In a right triangle, if the angle opposite the hypotenuse is 30 degrees and the adjacent side is 10 cm, what is the length of the opposite side?

  1. 5 cm

  2. 10 cm

  3. 15 cm

  4. 20 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a 30-60-90 triangle, the ratio of the opposite side to the hypotenuse is 1:2. Therefore, the length of the opposite side is (1/2) * 10 cm = 5 cm.

Multiple choice

In a triangle ABC, the sides AB and AC are 6 cm and 8 cm respectively. If the triangle is similar to triangle DEF, where DE is 9 cm, what is the length of DF?

  1. 12 cm

  2. 15 cm

  3. 18 cm

  4. 21 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/DE = AC/DF. Substituting the given values, we get 6/9 = 8/DF. Solving for DF, we get DF = 18 cm.

Multiple choice

Two triangles have corresponding sides of 3 cm, 4 cm, and 5 cm, and 6 cm, 8 cm, and 10 cm respectively. Are the triangles similar?

  1. Yes

  2. No
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To determine if the triangles are similar, we need to check if the ratios of their corresponding sides are equal. The ratios are 3/6 = 1/2, 4/8 = 1/2, and 5/10 = 1/2. Since all the ratios are equal, the triangles are similar.

Multiple choice

In a right triangle ABC, the hypotenuse AB is 10 cm and the side AC is 6 cm. If triangle PQR is similar to triangle ABC, where PQ is 15 cm, what is the length of QR?

  1. 9 cm

  2. 12 cm

  3. 15 cm

  4. 18 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/PQ = AC/QR. Substituting the given values, we get 10/15 = 6/QR. Solving for QR, we get QR = 12 cm.

Multiple choice

In a right triangle ABC, the hypotenuse AB is 20 cm and the side AC is 12 cm. If triangle PQR is similar to triangle ABC, where PQ is 30 cm, what is the length of QR?

  1. 18 cm

  2. 24 cm

  3. 30 cm

  4. 36 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/PQ = AC/QR. Substituting the given values, we get 20/30 = 12/QR. Solving for QR, we get QR = 24 cm.