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This mock test of Triangles - Olympiad Level MCQ, Class 10 Mathematics for Class 10 helps you for every Class 10 entrance exam.
This contains 25 Multiple Choice Questions for Class 10 Triangles - Olympiad Level MCQ, Class 10 Mathematics (mcq) to study with solutions a complete question bank.
The solved questions answers in this Triangles - Olympiad Level MCQ, Class 10 Mathematics quiz give you a good mix of easy questions and tough questions. Class 10
students definitely take this Triangles - Olympiad Level MCQ, Class 10 Mathematics exercise for a better result in the exam. You can find other Triangles - Olympiad Level MCQ, Class 10 Mathematics extra questions,
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QUESTION: 1

If the medians of a triangle are equal, then the triangle is:

Solution:

QUESTION: 2

The incentre of a triangle is determined by the:

Solution:

QUESTION: 3

The point of intersection of the angle bisectors of a triangle is :

Solution:

QUESTION: 4

A triangle PQR is formed by joining the mid-points of the sides of a triangle ABC. 'O' is the circumcentre of

ΔABC, then for ΔPQR, the point 'O' is :

Solution:

QUESTION: 5

If AD, BE, CF are the altitudes of ΔABC whose orthocentre is H, then C is the orthocentre of :

Solution:

QUESTION: 6

In an equilateral ΔABC, if a, b and c denote the lengths of perpendiculars from A, B and C respectively on the opposite sides, then:

Solution:

QUESTION: 7

Any two of the four triangles formed by joining the midpoints of the sides of a given triangle are:

Solution:

QUESTION: 8

The internal bisectors of ∠B and ∠C of ΔABC meet at O. If ∠A = 80° then ∠BOC is :

Solution:

QUESTION: 9

The point in the plane of a triangle which is at equal perpendicular distance from the sides of the triangle is :

Solution:

QUESTION: 10

Incentre of a triangle lies in the interior of :

Solution:

QUESTION: 11

In a triangle PQR, PQ = 20 cm and PR = 6 cm, the side QR is :

Solution:

QUESTION: 12

If ABC is a right angled triangle at B and M, N are the mid-points of AB and BC, then 4 (AN^{2} + CM^{2}) is equal to–

Solution:

QUESTION: 13

ABC is a right angle triangle at A and AD is perpendicular to the hypotenuse. Then BD/CD is equal to :

Solution:

QUESTION: 14

Let ABC be an equilateral triangle. Let BE . CA meeting CA at E, then (AB2 + BC2 + CA2) is equal to :

Solution:

QUESTION: 15

If D, E and F are respectively the mid-points of sides of BC, CA and AB of a ΔABC. If EF = 3 cm, FD =

4 cm, and AB = 10 cm, then DE, BC and CA respectively will be equal to :

Solution:

QUESTION: 16

In the right angle triangle ∠C = 90°. AE and BD are two medians of a triangle ABC meeting at F. The ratio

of the area of ΔABF and the quadrilateral FDCE is :

Solution:

QUESTION: 17

The bisector of the exterior ∠A of ΔABC intersects the side BC produced to D. Here CF is parallel to AD.

Solution:

QUESTION: 18

The diagonal BD of a quadrilateral ABCD bisects ∠B and ∠D, then:

Solution:

QUESTION: 19

Two right triangles ABC and DBC are drawn on the same hypotenuse BC on the same side of BC. If AC and

DB intersects at P, then

Solution:

QUESTION: 20

In figure, ABC is a right triangle, right angled at B. AD and CE are the two medians drawn from A and C

respectively. If AC = 5 cm and AD = cm, find the length of CE:

Solution:

Given: A triangle ABC right angled at B. AD and CE and medians drawn from vertices A and C respectively.

To find: CE = ?

In ∆ABD, AD^{2} = AB^{2} + BD^{2}

[Using Pythagoras theorem]

QUESTION: 21

In a ΔABC, AB = 10 cm, BC = 12 cm and AC = 14 cm. Find the length of median AD. If G is the centroid,

find length of GA :

Solution:

QUESTION: 22

The three sides of a triangles are given. Which one of the following is not a right triangle?

Solution:

QUESTION: 23

In the figure AD is the external bisector of ∠EAC, intersects BC produced to D. If AB = 12 cm, AC = 8 cm

and BC = 4 cm, find CD.

Solution:

QUESTION: 24

In ΔABC, AB^{2 }+ AC^{2} = 2500 cm^{2} and median AD = 25 cm, find BC.

Solution:

QUESTION: 25

In the given figure, AB = BC and ∠BAC = 15°, AB = 10 cm. Find the area of ΔABC.

Solution:

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