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SSC > Geometry

Explore popular questions from Geometry for SSC. This collection covers Geometry previous year SSC questions hand picked by experienced teachers.

Q 1.

Correct4

Incorrect-1

The in-radius of an equilateral triangle is of length {tex} 3 \mathrm { cm } . {/tex} Then the length of each of its medians is

A

{tex} 12 \mathrm { cm } {/tex}

B

{tex} \frac { 9 } { 2 } \mathrm { cm } {/tex}

C

{tex} 4 \mathrm { cm } {/tex}

{tex} 9 \mathrm { cm } {/tex}

Explanation


Q 2.

Correct4

Incorrect-1

If the orthocentre and the centroid of a triangle are the same, then the triangle is :

A

Scalene

B

Right angled

Equilateral

D

Obtuse angled

Explanation

Q 3.

Correct4

Incorrect-1

If in a triangle, the circumcentre, incentre, centroid and orthocentre coincide, then the triangle is

A

Acute angled

B

Isosceles

C

Right angled

Equilateral

Explanation

Q 4.

Correct4

Incorrect-1

In a triangle, if three altitudes are equal, then the triangle is

A

Obtuse

Equilateral

C

Right

D

Isosceles

Explanation

Q 5.

Correct4

Incorrect-1

If {tex} \mathrm { ABC } {/tex} is an equilateral triangle and {tex} \mathrm { D } {/tex} is a point on {tex} \mathrm { BC } {/tex} such that {tex} \mathrm { AD } \perp \mathrm { BC } , {/tex} then

A

{tex} A B: B D = 1: 1 {/tex}

B

{tex} A B: B D = 1: 2 {/tex}

{tex} A B: B D = 2: 1 {/tex}

D

{tex} A B: B D = 3: 2 {/tex}

Explanation

Q 6.

Correct4

Incorrect-1

The side {tex} \mathrm { QR } {/tex} of an equilateral tri- angle {tex} \mathrm { PQR } {/tex} is produced to the point {tex} \mathrm { S } {/tex} in such a way that {tex} \mathrm { QR } = \mathrm { RS } {/tex} and {tex} \mathrm { P } {/tex} is joined to {tex} \mathrm {S}{/tex}. Then the measure of {tex} \angle \mathrm { PSR } {/tex} is

{tex} 30 ^ { \circ } {/tex}

B

{tex} 15 ^ { \circ } {/tex}

C

{tex} 60 ^ { \circ } {/tex}

D

{tex} 45 ^ { \circ } {/tex}

Explanation


Q 7.

Correct4

Incorrect-1

If the circumradius of an equilateral triangle be {tex} 10 \mathrm { cm } , {/tex} then the measure of its in-radius is

{tex} 5 \mathrm { cm } {/tex}

B

{tex} 10 \mathrm { cm } {/tex}

C

{tex} 20 \mathrm { cm } {/tex}

D

{tex} 15 \mathrm { cm } {/tex}

Explanation



Q 8.

Correct4

Incorrect-1

If the incentre of an equilateral triangle lies inside the triangle and its radius is {tex} 3 \mathrm { cm } , {/tex} then the side of the equilateral triangle is

A

{tex} 9 \sqrt { 3 } \mathrm { cm } {/tex}

{tex} 6 \sqrt { 3 } \mathrm { cm } {/tex}

C

{tex} 3 \sqrt { 3 } \mathrm { cm } {/tex}

D

{tex} 6 \mathrm { cm } {/tex}

Explanation

Q 9.

Correct4

Incorrect-1

In a triangle, if orthocentre, circumcentre, incentre and centroid coincide, then the triangle must be

A

obtuse angled

B

isosceles

equilateral

D

right-angled

Explanation

Q 10.

Correct4

Incorrect-1

If {tex} \mathrm { ABC } {/tex} is an equilateral triangle and {tex} \mathrm { P } {/tex},{tex} \mathrm { Q } ,\mathrm R{/tex} respectively denote the middle points of {tex} \mathrm { AB } , \mathrm { BC } , \mathrm { CA } {/tex} then.

{tex}\mathrm{PQR}{/tex} must be an equilateral triangle

B

{tex} \mathrm { PQ } + \mathrm { QR } + \mathrm { PR } = \mathrm { AB } {/tex}

C

{tex} \mathrm { PQ } + \mathrm { QR } + \mathrm { PR } = 2 \mathrm { AB } {/tex}

D

{tex}\mathrm{PQR}{/tex} must be a right angled triangle

Explanation

Q 11.

Correct4

Incorrect-1

Let {tex}ABC{/tex} be an equilateral triangle and {tex}AX, BY, CZ{/tex} be the altitudes. Then the right statement out of the four given responses is

{tex} A X = B Y = C Z {/tex}

B

{tex} A X \neq B Y = C Z {/tex}

C

{tex} A X = B Y \neq C Z {/tex}

D

{tex} A X \neq B Y \neq C Z {/tex}

Explanation


Q 12.

Correct4

Incorrect-1

{tex} \mathrm { ABC } {/tex} is an equilateral triangle and {tex} \mathrm { CD } {/tex} is the internal bisector of {tex} \angle {/tex} {tex} \mathrm { C } . {/tex} If {tex} \mathrm { DC } {/tex} is produced to {tex} \mathrm { E } {/tex} such that {tex} \mathrm { AC } = \mathrm { CE } , {/tex} then {tex} \angle \mathrm { CAE } {/tex} is equal to

A

{tex} 45 ^ { \circ } {/tex}

B

{tex} 75 ^ { \circ } {/tex}

C

{tex} 30 ^ { \circ } {/tex}

{tex} 15 ^ { \circ } {/tex}

Explanation


Q 13.

Correct4

Incorrect-1

{tex} \mathrm {G}{/tex} is the centroid of the equilateral {tex} \Delta \mathrm { ABC } {/tex}. If {tex} \mathrm { AB } = 10 \mathrm { cm } {/tex} then length of {tex} \mathrm { AG } {/tex} is

A

{tex} \frac { 5 \sqrt { 3 } } { 3 } \mathrm { cm } {/tex}

{tex} \frac { 10 \sqrt { 3 } } { 3 } \mathrm { cm } {/tex}

C

{tex} 5 \sqrt { 3 } \mathrm { cm } {/tex}

D

{tex} 10 \sqrt { 3 } \mathrm { cm } {/tex}

Explanation


Q 14.

Correct4

Incorrect-1

The radius of the incircle of the equilateral triangle having each side {tex} 6 \mathrm { cm } {/tex} is

A

{tex} 2 \sqrt { 3 } \mathrm { cm } {/tex}

{tex} \sqrt { 3 } \mathrm { cm } {/tex}

C

{tex} 6 \sqrt { 3 } \mathrm { cm } {/tex}

D

{tex} 2 \mathrm { cm } {/tex}

Explanation


Q 15.

Correct4

Incorrect-1

If the three medians of a triangle are same then the triangle is

equilateral

B

isosceles

C

right-angled

D

obtuse-angle

Explanation

Q 16.

Correct4

Incorrect-1

If in a triangle {tex} \mathrm { ABC } {/tex} as drawn in the figure, {tex} \mathrm { AB } = \mathrm { AC } {/tex} and {tex} \angle \mathrm { ACD } = {/tex} {tex} 120 ^ { \circ } {/tex}, then {tex} \angle \mathrm { A } {/tex} is equal to

A

{tex} 50 ^ { \circ } {/tex}

{tex} 60 ^ { \circ } {/tex}

C

{tex} 70 ^ { \circ } {/tex}

D

{tex} 80 ^ { \circ } {/tex}

Explanation


Q 17.

Correct4

Incorrect-1

The side {tex} \mathrm { BC } {/tex} of a triangle {tex} \mathrm { ABC } {/tex} is extended to {tex} \mathrm { D } {/tex}. If {tex} \angle \mathrm { ACD } = 120 ^ { \circ } {/tex}and {tex} \angle \mathrm { ABC } = \frac { 1 } { 2 } \angle \mathrm { CAB } , {/tex} then the value of {tex} \angle \mathrm { ABC } {/tex} is

A

{tex} 80 ^ { \circ } {/tex}

{tex} 40 ^ { \circ } {/tex}

C

{tex} 60 ^ { \circ } {/tex}

D

{tex} 20 ^ { \circ } {/tex}

Explanation


Q 18.

Correct4

Incorrect-1

For an equilateral triangle, the ratio of the in-radius and the ex-radius is

{tex}1:2{/tex}

B

{tex} 1: \sqrt { 2 } {/tex}

C

{tex}1:3{/tex}

D

{tex} 1: \sqrt { 3 } {/tex}

Explanation

Q 19.

Correct4

Incorrect-1

If the three angles of a triangle are :
{tex} \left( x + 15 ^ { \circ } \right) , \left( \frac { 6 x } { 5 } + 6 ^ { \circ } \right) {/tex} and {tex} \left( \frac { 2 x } { 3 } + 30 ^ { \circ } \right) , {/tex} then the triangle is :

A

isosceles

B

right angled

equilateral

D

scalene

Explanation


Q 20.

Correct4

Incorrect-1

Let {tex} \mathrm { ABC } {/tex} be an equilateral triangle and {tex} \mathrm { AD}{/tex} perpendicular to {tex} \mathrm { BC}{/tex}. Then {tex} \mathrm { AB } ^ { 2 } + \mathrm { BC } ^ { 2 } + \mathrm { CA } ^ { 2 } = ? {/tex}

A

{tex} 2 \mathrm { AD } ^ { 2 } {/tex}

B

{tex} 3 \mathrm { AD } ^ { 2 } {/tex}

{tex} 4 \mathrm { AD } ^ { 2 } {/tex}

D

{tex} 5 \mathrm { AD } ^ { 2 } {/tex}

Explanation


Q 21.

Correct4

Incorrect-1

The centroid of an equilateral triangle {tex} \mathrm { ABC } {/tex} is {tex} \mathrm { G } {/tex} and {tex} \mathrm { AB } = 10 \mathrm { cm } . {/tex} The length of {tex} \mathrm { AG } ( \text { in } \mathrm { cm } ) {/tex} is :

A

{tex} 3 \frac { 1 } { 3 } {/tex}

B

{tex} \frac { 10 } { \sqrt { 3 } } {/tex}

{tex} \frac { 10 \sqrt { 3 } } { 3 } {/tex}

D

{tex} \frac { \sqrt { 3 } } { 3 } {/tex}

Explanation





Q 22.

Correct4

Incorrect-1

Let {tex} \mathrm { AX}{/tex} {tex} \perp {/tex} {tex} \mathrm { BC}{/tex} of an equilateral triangle {tex} \mathrm { ABC}{/tex}. Then the sum of the perpendicular distances of the sides of {tex} \mathrm { \triangle A B C }{/tex} from any point inside the triangle is:

A

Equal to {tex} \mathrm { BC}{/tex}

Equal to {tex} \mathrm { AX}{/tex}

C

Less than {tex} \mathrm { AX}{/tex}

D

Greater than {tex} \mathrm { AX}{/tex}

Explanation





Q 23.

Correct4

Incorrect-1

Let {tex}G{/tex} be the centroid of the equilateral triangle {tex}ABC{/tex} of perimeter {tex} 24 \mathrm { cm } . {/tex} Then the length of {tex}AG{/tex} is

A

{tex} 2 \sqrt { 3 } \mathrm { cm } {/tex}

{tex} \frac { 8 } { \sqrt { 3 } } \mathrm { cm } {/tex}

C

{tex} 8 \sqrt { 3 } \mathrm { cm } {/tex}

D

{tex} 4 \sqrt { 3 } \mathrm { cm } {/tex}

Explanation


Q 24.

Correct4

Incorrect-1

{tex} \mathrm { O}{/tex} is the orthocentre of {tex} \triangle \mathrm { ABC } , {/tex} and if {tex} \angle \mathrm { BOC } = 110 ^ { \circ } , {/tex} then {tex} \angle \mathrm { BAC } {/tex} will be

A

{tex} 110 ^ { \circ } {/tex}

{tex} 70 ^ { \circ } {/tex}

C

{tex} 100 ^ { \circ } {/tex}

D

{tex} 90 ^ { \circ } {/tex}

Explanation


Q 25.

Correct4

Incorrect-1

The altitude of an equilateral triangle of side {tex} \frac { 2 } { \sqrt { 3 } } \quad \mathrm { cm } {/tex} is :

A

{tex} \frac { 4 } { 3 } \mathrm { m } {/tex}

B

{tex} \frac { 4 } { \sqrt { 3 } } \mathrm { m } {/tex}

C

{tex} \frac { 4 } { 3 } \mathrm { m } {/tex}

{tex} 1 \mathrm { m } {/tex}

Explanation