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

If radius of circle is 1 cm ,what would be side of square ABCD If B lies on circle and AC is tangent of circle. यदि वृत्त की त्रिज्या 1 सेमी हो, तब वर्ग ABCD की भुजा की लम्बाई क्या होगी? यदि B और D वृत्त पर हो और AC वृत्त की स्पर्श रेखा हो।

  1. 1.2

  2. 1.6

  3. 1.8

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

This problem describes a geometric configuration but is underspecified without the diagram. Based on the answer choice 1.6 (B), this likely involves a specific configuration where vertices B and D lie on the circle of radius 1, and diagonal AC is tangent to the circle. The geometry suggests a relationship between the circle's radius and the square's side that yields approximately 1.6 cm. However, the exact configuration matters - different positions of B and D on the circle would yield different answers.

Multiple choice

At the centres of two circles, two arcs of equal length subtend angles of 450 and 750 respectively, the ratio of the radii of the two circles is- दो वृत्तों के केंद्रों पर दो बराबर लम्बाई की चापें क्रमशः 450 और 750 के कोण बनाती है। तद्नुसार उन दोनों वृत्तों की त्रिज्याओं का अनुपात कितना होगा?

  1. 5 : 3

  2. 3 : 5

  3. 1 : 5

  4. 1 : 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Arc length l = r × θ (where θ is in radians). For equal arc lengths: r₁ × θ₁ = r₂ × θ₂. Therefore r₁/r₂ = θ₂/θ₁ = 75/45 = 5/3. So the ratio is 5:3.

Multiple choice

If O is the circumcentre of ΔABC and ∠OBC = 400, then the ∠BAC is equal to. यदि O, ΔABC का परिकेन्द्र है और ∠OBC = 400, तो ∠BAC है।

  1. 500

  2. 800

  3. 640

  4. 620
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If O is circumcenter of ΔABC, then O is equidistant from all vertices, so OA = OB = OC = R (circumradius). In ΔOBC, ∠OBC = 40° and OB = OC, so ∠OCB = 40°. Then ∠BOC = 180° - 2×40° = 100°. At circumcenter, central angle is twice inscribed angle: ∠BOC = 2∠BAC. So 100° = 2∠BAC, giving ∠BAC = 50°.

Multiple choice

An arc of length 37.4 cm inercepts angle 600 at centre find the radius of the circle- एक 37.4 सेमी. लंबाई का चाप केन्द्र पर 600 का कोण अन्तरित करता है तो वृत्त की त्रिज्या ज्ञात कीजिए।

  1. 35.2 cm./सेमी.

  2. 37.4 cm./सेमी.

  3. 35.7 cm./सेमी.

  4. 35.00 cm./सेमी.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Arc length formula: l = (θ/360) × 2πr, where θ is in degrees. Given l = 37.4 cm and θ = 60° (not 600° - typo in question). So 37.4 = (60/360) × 2πr = (π/3)r, giving r = 37.4 × 3/π. Using π ≈ 3.14: r ≈ 112.2/3.14 ≈ 35.7 cm.

Multiple choice

If the arcs of the same lengths in two circles subtends angles 650 and 1100 at the centre, find the ratio of their radii? यदि दो वृत्त के चापों की लंबाई समान हो और वे अपने केंद्र पर क्रमशः 650 और 1100 का कोण बनाते है, तो उनकी त्रिज्याओं का अनुपात ज्ञात कीजिये-

  1. 22 : 13

  2. 22 : 19

  3. 11 : 13

  4. 13 : 22
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For equal arc lengths: l1 = l2, so (θ1/360) × 2πr1 = (θ2/360) × 2πr2, giving θ1r1 = θ2r2. So r1/r2 = θ2/θ1 = 1100/650 = 22/13. Ratio of radii is 22:13.

Multiple choice

Find the area of a square inscribed in a circle of radius 5 cm. 5 सेमी त्रिज्या वाले वृत्त में खींचे गये वृत्त का क्षेत्रफल ज्ञात कीजिए।

  1. 25 cm2 /सेमी2

  2. 35 cm2 /सेमी2

  3. 50 cm2 /सेमी2

  4. 65 cm2 /सेमी2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When a square is inscribed in a circle, the diagonal of the square equals the diameter of the circle. Circle radius = 5 cm, so diameter = 10 cm. Let square side = s. By Pythagorean theorem, diagonal² = s² + s² = 2s². So s² = diagonal²/2 = 100/2 = 50. Area of square = s² = 50 sq cm. Option C is correct.

Multiple choice

A right angled triangle has perimeter 32 cm and area 20 cm2 what is the length of its hypotenuse. एक समकोण त्रिभुज का परिमाप 32 सेमी. है और क्षेत्रफल 20 सेमी2 है | इसके कर्ण की लम्बाई क्या है ?

  1. 14.75 cm./सेमी.

  2. 15.21 cm./सेमी.

  3. 13.24 cm./सेमी.

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

For right triangle with sides a, b, c (hypotenuse): a + b + c = 32, ab = 40 (from area = 20), and a² + b² = c². Solving: (32-c)² = c² + 80, giving 1024 - 64c = 80, so c = 14.75 cm. Option A is correct. Options B and C don't satisfy the Pythagorean theorem with the given constraints.

Multiple choice

There is a semi-circle with diameter AD = 8 cm and a chord BC ||AD. AB = CD = 2 cm. Find the measure of BC एक अर्द्धवृत्त जिसका व्यास 8 बउ है। और एवं जीवा BC है | AD. AB = CD = 2, BC की माप ज्ञात करो।

  1. 11 cm./सेमी.

  2. 9 cm./सेमी.

  3. 5 cm./सेमी.

  4. 7 cm./सेमी.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In the semicircle, drop perpendiculars from B and C to diameter AD. Let the foot from B be E and from C be F. AB = CD = 2, so AE = DF = 2. Radius = 4, so the perpendicular heights equal √(4² - 2²) = √12. By symmetry, BC = 2√12 = 2×3.46 = 6.92 ≈ 7 cm. Option D is correct. Options A, B, C don't satisfy the geometric constraints.

Multiple choice

In a circle center O (0, r) , two tangents drawn from point A touches circle at point P, Q. If ∠PAQ= 48o then find the ∠APQ? O केन्द्र वाले वृत्त में बिन्दु वाले वृत्त पर बिंदु A से दो स्पर्श रेखा खिची जाती है व्रत को P और Q पर स्पर्श करती है यदि ∠PAQ= 48o तो ∠APQ मान कितना होगा ?

  1. 96o

  2. 66o

  3. 60o

  4. 48o
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Tangents from an external point to a circle are equal (AP = AQ), making triangle APQ isosceles. The line from the center O to the external point A bisects ∠PAQ, so ∠PAO = 48°/2 = 24°. Since AP = AQ, triangle APQ is isosceles with ∠APQ = ∠AQP = (180° - 48°)/2 = 66°. Alternatively, using right triangle APO: ∠AOP = 180° - 90° - 24° = 66°.

Multiple choice

Chords AB, BC, CD subtend angles of 80o, 60o and 70o respectively at the center O of the circle then the acute angle between AC and BD is- जीवा AB, BC, CD जिनका केन्द्र O के साथ कोण क्रमशः 80o, 60o और 70o है तो AC और BD के मध्य न्यून कोण होगा ?

  1. 60o

  2. 75o

  3. 65o

  4. 80o
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Angles subtended by equal chords are equal. Let angle AOB = 80°, BOC = 60°, COD = 70°. Then AOC = AOB + BOC = 140° and BOD = BOC + COD = 130°. Let AC and BD intersect at P. In triangle APB: angle APB = 180° - angle PAB - angle PBA = 180° - 70° - 65° = 45°. The acute angle between AC and BD is angle APB + angle BPC (vertically opposite) = 45° + 30° = 75°. Alternatively, using angle bisector properties at intersection P.

Multiple choice

The in-radius of an equilateral triangle is of length 3 cm. Then the length of each of its median is- किसी समबाहु त्रिभुज की आंतरिक त्रिज्या 3 सेमी है तो इसकी प्रत्येक मध्यिका ज्ञात करें ?

  1. 12

  2. 9/2

  3. 4

  4. 9
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For an equilateral triangle, inradius r = a/(2√3), where a is side length. Given r = 3 cm, we get a = 6√3 cm. In an equilateral triangle, median = altitude = a√3/2. Substituting a = 6√3, we get median = (6√3 × √3)/2 = (6 × 3)/2 = 9 cm. Option D is correct.

Multiple choice

The length of two chords situated at the opposite sides of the centre of a circle having diameter 20 cm are 16 cm and 12 cm respectively. Then the distance between them is- 20 सेमी व्यास वाले एक वृत्त के केंद्र की विपरीत दिशाओं में स्थित दो जीवाओं की लंबाई क्रमशः 16 सेमी और 12 सेमी हैं तो उनके बीच दूरी है?

  1. 14 cm/ सेमी

  2. 10 cm/ सेमी

  3. 12 cm/ सेमी

  4. 8 cm/ सेमी
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Circle diameter = 20 cm, so radius = 10 cm. For 16 cm chord, distance from center = sqrt(10² - 8²) = 6 cm. For 12 cm chord, distance = sqrt(10² - 6²) = 8 cm. Since chords are on opposite sides of center, total distance between them = 6 + 8 = 14 cm. Use perpendicular distance formula from center to chord.

Multiple choice

The length of the common chord of two intersecting circles in 24 cm. If the diameter of the circles are 30 cm and 26 cm respectively. Then the distance between the center (in cm.) is- दो प्रतिच्छेदित वृत्त की उभयनिष्ठ जीवा की लम्बाई 24 सेमी हो, यदि दोनों वृत्तों के व्यास क्रमशः 30 सेमी तथा 26 सेमी है। तब उनके केन्द्रों के बीच की दूरी ज्ञात करें ?

  1. 13

  2. 14

  3. 15

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

For circle 1 (radius 15 cm), distance from center to chord = √(15² - 12²) = 9 cm. For circle 2 (radius 13 cm), distance from center to chord = √(13² - 12²) = 5 cm. Total distance between centers = 9 + 5 = 14 cm.

Multiple choice

Two chords AB and CD of a circle with centre O intersect each other at the point P. If ∠AOD = 20o and ∠BOC = 30o. Then ∠BPC is equal to- O केन्द्र वाले वृत्त की दो जीवायें AB तथा CD एक दूसरे को बिन्दू P पर प्रतिच्छेदित करती है। यदि ∠AOD = 20o और ∠BOC = 30o तब ∠BPC बराबर है-

  1. 50o

  2. 20o

  3. 25o

  4. 30o
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For intersecting chords, ∠BPC = (1/2)(arc BC + arc AD). Central angle ∠AOD = 20° subtends arc AD, so arc AD = 20°. Central angle ∠BOC = 30° subtends arc BC, so arc BC = 30°. Therefore ∠BPC = (1/2)(20° + 30°) = 25°.