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Arithmetic Ability
Triangles
Quiz 2
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Q.1
PQR is an equilateral triangle. MN is drawn parallel to QR such that M is on PQ and N is on PR. If PN = 6 cm, then the length of MN is:
3 cm
6 cm
12 cm
4.5 cm
Q.2
In ΔABC, ∠BAC = 90° and AD ⊥ BC. If BD = 3 cm and CD = 4 cm, then length of AD is :
$$2\sqrt 3 $$ cm
3.5 cm
6 cm
5 cm
Q.3
ABC is an isosceles triangle inscribed in a circle. If AB = AC = 12$$\sqrt 5 $$ and BC = 24 cm then radius of circle is:
10 cm
15 cm
12 cm
14 cm
Q.4
Let ABC be an equilateral triangle and AD perpendicular to BC, then AB
2
+ BC
2
+ CA
2
= ?
3AD
2
5AD
2
2AD
2
4AD
2
Q.5
Incenter of ΔABC is I. ∠ABC = 90° and ∠ACB = 70°. ∠BIC is:
115°
100°
110°
105°
Q.6
If in ΔABC, DE || BC, AB = 7.5 cm BD = 6 cm and DE = 2 cm then the length of BC in cm is:
6 cm
8 cm
10 cm
10.5 cm
Q.7
In a ΔPQR, ∠Q = 55° and ∠R = 35°. Find the ratio of angles subtended by side QR on circumcenter, incenter and orthocenter of the triangle.
3 : 2 : 1
3 : 2 : 4
3 : 2 : 4
4 : 3 : 2
Q.8
In ΔPQR, straight line parallel to the base QR cuts PQ at X and PR at Y. If PX : XQ = 5 : 6, then XY : QR will be
5 : 11
6 : 5
11 : 6
11 : 5
Q.9
In ΔABC, ∠B = 60° and ∠C = 40°; AD and AE are respectively the bisector of ∠A and perpendicular on BC. The measure of ∠EAD is:
9°
11°
10°
12°
Q.10
ABC is a triangle in which ∠A = 90°. Let P be any point on side AC. If BC = 10 cm, AC = 8 cm and BP = 9 cm, then AP = ?
$$2\sqrt 5 $$ cm
$$3\sqrt 5 $$ cm
$$2\sqrt 3 $$ cm
$$3\sqrt 3 $$ cm
Q.11
In ΔABC, the line parallel to BC intersect AB & AC at P & Q respectively. If AB : AP = 5 : 3, then AQ : QC is:
3 : 2
1 : 2
3 : 5
2 : 3
Q.12
∠A of ΔABC is a right angle. AD is perpendicular on BC. If BC = 14 and BD = 5 cm, then measure of AD is:
$$\sqrt 5 $$ cm
$$3\sqrt 5 $$ cm
$$3.5\sqrt 5 $$ cm
$$2\sqrt 5 $$ cm
Q.13
In ΔABC, if AD ⊥ BC, then AB
2
+ CD
2
is equal to
2BD
2
BD
2
+ AC
2
2AC
2
None of these
Q.14
In ΔABC, the external bisectors of the angles ∠B and ∠C meet at the point O. If ∠A = 70°, then the measure of ∠BOC is :
75°
50°
55°
60°
Q.15
If I be the incentre of ΔABC and ∠B = 70° and ∠C = 50°, then the magnitude of ∠BIC is
130°
60°
120°
105°
Q.16
In ΔABC, AD ⊥ BC and AD
2
= BD × DC. The measure of ∠BAC is :
75°
90°
45°
60°
Q.17
For a triangle ABC, D, E, F are the mid - point of its sides. If ΔABC = 24 sq. units then ΔDEF is :
4 sq. units
6 sq. units
8 sq. units
12 sq. units
Q.18
If two medians BE and CF of a triangle ABC, intersect each other at G and if BG = CG, ∠BGC = 60°, BC = 8 cm, then area of the triangle ABC is:
$$96\sqrt 3 $$ cm
2
$$48\sqrt 3 $$ cm
2
48 cm
2
$$54\sqrt 3 $$ cm
2
Q.19
In ΔABC, AB = BC = K, AC = $$\sqrt 2 $$ k, then ΔABC is a :
Right isosceles triangle
Isosceles triangle
Right-angled triangle
Equilateral triangle
Q.20
If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB = 19 cm and AC = 22 cm then the length of BC is :
20.5 cm
19.5 cm
26 cm
13 cm
Q.21
The sum of three altitudes of a triangle is
Equal to the sum of three sides
Less than the sum of sides
Greater than the sum of sides
Twice the sum of sides
Q.22
In a right-angled triangle, the product of two sides is equal to half of the square of the third side i.e., hypotenuse. One of the acute angle must be
60°
30°
45°
15°
Q.23
In ΔABC, ∠B = 60° and ∠C = 40°. If AD and AE be respectively the internal bisector of ∠A and perpendicular on BC, then the measure of ∠DAE is
5°
10°
40°
60°
Q.24
If the measures of the sides of triangle are (x
2
- 1), (x
2
+ 1) and 2x cm, then the triangle would be :
Equilateral
Acute-angled
Right-Angled
Isosceles
Q.25
In ΔABC, ∠C is an obtuse angle. The bisectors of the exterior angles at A and B meet BC and AC produced at D and E respectively. If AB = AD = BE, then ∠ACB = ?
105°
108°
110°
135°
Q.26
In ΔABC, DE || AC, D and E are two points on AB and CB respectively. If AB = 10 cm and AD = 4 cm, then BE : CE is
2 : 3
2 : 5
5 : 2
3 : 2
Q.27
Let ABC be an equilateral triangle and AX, BY, CZ be the altitude. Then the right statement out of the four give responses is :
AX = BY = CZ
AX ≠ BY = CZ
AX = BY ≠ CZ
AX ≠ BY ≠ CZ
Q.28
An isosceles triangle ABC is right-angled at B. D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the side AB and AC respectively of ΔABC. If AP = a cm, AQ = b cm and ∠BAD = 15°, sin 75° = ?
$$\frac{{2b}}{{\sqrt 3 a}}$$
$$\frac{a}{{2b}}$$
$$\frac{{\sqrt 3 a}}{{2b}}$$
$$\frac{{2a}}{{\sqrt 3 b}}$$
Q.29
If the sides of a right angled triangle are three consecutive integers, then the length of the smallest side is
3 units
2 units
4 units
5 units
Q.30
In a triangle ABC, the side BC is extended up to D such that CD = AC. If ∠BAD = 109° and ∠ACB = 72° then the value of ∠ABC is
35°
60°
40°
45°
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