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

The distance of a chord of length 16 cm from the centre of a circle of radius 10 cm is

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Multiple choice

The line $x\cos\alpha+y\sin\alpha=p$ intersects the circle $x^{2}+y^{2}=4$ at $A$ and $B$. If the chord $AB$ makes an angle $30^{o}$ at a point on the circumference of the circle, then:

$p^{2}=3$
$p^{2}=4\cos^{4}15^{o}$
$p^{2}=2$
$p^{2}=6$

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Multiple choice

A circle is inscribed in a square as shown below. If the radius of the circle is $4$ cm, then the perimeter of the square is ______

$28$ cm
$24$ cm
$32$ cm
$36$ cm

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Multiple choice

A chord of circle $14cm$ makes an angle of $60^o$ at the centre of the circle. Find (i) Area of minor sector (ii) Area of the major segment (iii)Area of the major sector (iv)Area of the major segment

$(i)=102.57cm^2, (ii)=17.80cm^2, (iii)=512.87cm^2, (iv)=597.64cm^2$
$(i)=12.57cm^2, (ii)=17.80cm^2, (iii)=512.87cm^2, (iv)=597.64cm^2$
$(i)=102.57cm^2, (ii)=1.80cm^2, (iii)=512.87cm^2, (iv)=597.64cm^2$
None of these

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Multiple choice

A chord of a circle of radius $7$ cm. subtends an angle of $90^o$ at its centre. The ratio of areas of smaller and larger segment is

$2:7$
$1:10$
$1:11$
none of these

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Multiple choice

A circle is inscribed in trapezoid $PQRS$. If $PS=QR=25\;cm,\,PQ=18\;cm\;and\;SR=32\;cm$, what is the length of the diameter of the circle ?

$14\;cm$
$25\;cm$
$24\;cm$
$\sqrt{674}\;cm$

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Multiple choice

A chord AB of circle of radius $14 cm$ makes an angle of $\displaystyle 60^{\circ} $ at the centre of the circle .The area of the minor segment of the circle is (Use $\displaystyle \pi =\frac{22}{7} $)

$\displaystyle \dfrac{308}{3}cm^{2} $
$\displaystyle \dfrac{208}{3}cm^{2} $
$\displaystyle \dfrac{108}{3}cm^{2} $
$\displaystyle \dfrac{408}{3}cm^{2} $

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Multiple choice

The distance between the two parallel chords of length 8 cm and 6 cm in a circle of diameter 10 cm if the chords lic on the same side of the centre is

1 cm
2 cm
3 cm
4 cm

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Multiple choice

An arc of circle subtends an angle of $ \displaystyle 30^{\circ} $ at the centre If the radius of the circle is 7 cm then length of the arc will be equal to -

$ \displaystyle 3\frac{1}{3} cm $
$ \displaystyle 3\frac{1}{2} cm $
$ \displaystyle 3\frac{2}{3} cm $
None of these

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Multiple choice

A circle is inscribed in a square of side $\sqrt 6$. What is the area of the circle?

$\displaystyle \frac{3}{2}\pi $
6$\displaystyle \pi $
$\displaystyle \pi $
9$\displaystyle \pi $

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Multiple choice

A circle is inscribed in a square of side length $6$. The area of the region inside the square but outside the circle is

$36\pi$
$26\pi - 9$
$26\pi - 36$
$36 - 9\pi$
$9\pi - 36$

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Multiple choice

Area of a sector of central angle $200^0$ of a circle is 770 $cm^2$. The length of the corresponding arc of this sector is

$ 73\frac { 1 }{ 3 } cm $
$ 156\frac { 1 }{ 3 } cm $
$ 7\frac { 1 }{ 3 } cm $
$ 22\frac { 1 }{ 3 } cm $

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Multiple choice

A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of $60^0$ at its centre. The radius of the circle is

$\frac{60}{\pi}$cm
$\frac{120}{\pi}$cm
$\frac{30}{\pi}$cm
$\frac{90}{\pi}$cm

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Multiple choice

In a circle, two arc of unequal length subtended angles in the ratio $5: 3$. If the smaller angle is $45^o,$ then the measure of other angle is:

$75^o$
$72^o$
$60^o$
$78^o$

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Multiple choice

If the chord $y=mx+1$ of the circle $x^2+y^2=1$ subtends an angle of measure $45^o$ at the major segment of the circle then $m=?$

$2$
$-1$
$-2$
$3$

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