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Arithmetic Ability
Triangles
Quiz 4
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Q.1
In ΔABC, ∠BAC = 90° and AB = $$\frac{1}{2}$$ BC, Then the measure of ∠ACB is :
60°
30°
45°
15°
Q.2
If the length of the sides of a triangle are in the ratio 4 : 5 : 6 and the inradius of the triangle is 3 cm, then the altitude of the triangle corresponding to the largest side as base is :
7.5 cm
6 cm
10 cm
8 cm
Q.3
In triangle PQR, points A, B and C are taken on PQ, PR and QR respectively such that QC = AC and CR = CB. If ∠QPR = 40°, then ∠ACB is equal to:
140°
40°
70°
100°
Q.4
I is the incentre of a triangle ABC. If ∠ACB = 55°, ∠ABC = 65° then the value of ∠BIC is
130°
120°
140°
110°
Q.5
The length of the three sides of a right angled triangle are (x - 2) cm, (x) cm and (x + 2) cm respectively. Then the value of x is
10
8
4
0
Q.6
In a right angled ΔABC, ∠ABC = 90°, AB = 3, BC = 4, CA = 5; BN is perpendicular to AC, AN : NC is
3 : 4
9 : 16
3 : 16
1 : 4
Q.7
The length of the two sides forming the right angle of a right angled triangle are 6 cm and 8 cm. The length of its circum-radius is :
5 cm
7 cm
6 cm
10 cm
Q.8
In a triangle ABC, incentre is O and ∠BOC = 110°, then the measure of ∠BAC is:
20°
40°
55°
110°
Q.9
D is any point on side AC of ΔABC. If P, Q, X, Y are the mid-point of AB, BC, AD and DC respectively, then the ratio of PX and QY is
1 : 2
1 : 1
2 : 1
2 : 3
Q.10
For a triangle base is 6$$\sqrt 3 $$ cm and two base angles are 30° and 60°. Then height of the triangle is
3$$\sqrt 3 $$ cm
4.5 cm
4$$\sqrt 3 $$ cm
2$$\sqrt 3 $$ cm
Q.11
ΔABC is an isosceles triangle and $$\overline {AB} $$ = $$\overline {AC} $$ = 2a unit, $$\overline {BC} $$ = a unit. Draw $$\overline {AD} $$ ⊥ $$\overline {BC} $$ , and find the length of $$\overline {AD} $$
$$\sqrt {15} $$ a unit
$$\frac{{\sqrt {15} }}{2}$$ a unit
$$\sqrt {17} $$ a unit
$$\frac{{\sqrt {17} }}{2}$$ a unit
Q.12
If ABC is an equilateral triangle and D is a point of BC such that AD ⊥ BC, then
AB : BD = 1 : 1
AB : BD = 1 : 2
AB : BD = 2 : 1
AB : BD = 3 : 2
Q.13
ABC is an isosceles triangle with AB = AC, A circle through B touching AC at the middle point intersects AB at P. Then AP : AB is:
4 : 1
2 : 3
3 : 5
1 : 4
Q.14
ABC is a triangle. The bisectors of the internal angle ∠B and external angle ∠C intersect at D. If ∠BDC = 50°, then ∠A is
100°
90°
120°
60°
Q.15
AD is the median of a triangle ABC and O is the centroid such that AO = 10 cm. The length of OD (in cm) is
4 cm
5 cm
6 cm
8 cm
Q.16
In a triangle ABC, AB + BC = 12 cm, BC + CA = 14 cm and CA + AB = 18 cm. Find the radius of the circle (in cm) which has the same perimeter as the triangle
$$\frac{5}{2}$$
$$\frac{7}{2}$$
$$\frac{9}{2}$$
$$\frac{{11}}{2}$$
Q.17
In ΔABC, D and E are points on AB and AC respectively such that DE || BC and DE divides the ΔABC into two parts of equal areas. Then ratio of AD and BD is
1 : 1
1 : $$\sqrt 2 $$ - 1
1 : $$\sqrt 2 $$
1 : $$\sqrt 2 $$ + 1
Q.18
O is the incentre of ΔABC and ∠A = 30°, then ∠BOC is
100°
105°
110°
90°
Q.19
The side QR of an equilateral triangle PQR is produced to the point S in such a way that QR = RS and P is joined to S. Then the measure of ∠PSR is
30°
15°
60°
45°
Q.20
In a triangle ABC, AB = AC, ∠BAC = 40° then the external angle at B is :
90°
70°
110°
80°
Q.21
If the length of the three sides of a triangle are 6 cm, 8 cm and 10 cm, then the length of the median to its greatest side is -
8 cm
6 cm
5 cm
4.8 cm
Q.22
If ΔABC is an isosceles triangle with ∠C = 90° and AC = 5 cm then AB is:
5 cm
10 cm
5$$\sqrt 2 $$ cm
2.5 cm
Q.23
If the median drawn on the base of a triangle is half of its base the triangle will be
Right-angled
Acute-angled
Obtuse-angled
Equilateral
Q.24
In a triangle ABC, ∠BAC = 90° and AD is perpendicular to BC. If AD = 6 cm and BD = 4 cm then the length of BC is:
8 cm
10 cm
9 cm
13 cm
Q.25
I is the incentre of ΔABC. If ∠ABC = 60°, ∠BCA = 80°, then the ∠BIC is
90°
100°
110°
120°
Q.26
The angle between the external bisectors of two angles of a triangle is 60°. Then the third angle of the triangle is
40°
50°
60°
80°
Q.27
The circumcentre of a triangle ABC is O. If ∠BAC = 85° and ∠BCA = 75°, then the value of ∠OAC is
40°
60°
70°
90°
Q.28
In ΔABC ∠A = 90° and AD ⊥ BC where D lies on BC. If BC = 8 cm, AD = 6 cm, then arΔABC : arΔACD = ?
4 : 3
25 : 16
16 : 9
25 : 9
Q.29
Let O be the in-centre of a triangle ABC and D be a point on the side BC of ΔABC, such that OD ⊥ BC. If ∠BOD = 15°, then ∠ABC = ?
75°
45°
150°
90°
Q.30
The sides of a triangle are in the ratio 3 : 4 : 6. The triangle is:
Acute-angled
Right-angled
Obtuse-angled
Either acute-angled or right-angled
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