Geometry

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51 The sides of a triangle are in the ratio 3 : 4 : 6. The triangle is:

A
Acute-angled
B
Right-angled
C
Obtuse-angled
D
Either acute-angled or right-angled

52 In a triangle ABC, ∠A = 70°, ∠B = 80° and D is the incenter of ΔABC, ∠ACB = 2x° and ∠BDC = y°. The values of x and y, respectively are:

A
15°, 130°
B
15°, 125°
C
35°, 40°
D
30°, 150°

53 Angle between the internal bisectors of two angles of a triangle ∠B and ∠C is 120°, then ∠A is :

A
20°
B
30°
C
60°
D
90°

54 G is the centroid of the equilateral ΔABC. If AB = 10 cm then length of AG is ?

A
$$\frac{{5\sqrt 3 }}{3}\,cm$$
B
$$\frac{{10\sqrt 3 }}{3}\,cm$$
C
$$5\sqrt 3 \,cm$$
D
$$10\sqrt 3 \,cm$$

55 In an equilateral triangle ABC, G is the centroid. Each side of the triangle is 6 cm. The length of AG is:

A
$$2\sqrt 2 $$  cm
B
$$3\sqrt 2 $$  cm
C
$$2\sqrt 3 $$  cm
D
$$3\sqrt 3 $$  cm

56 Perimeter of a △ with integer sides is equal to 15. How many such triangles are possible?

A
7
B
6
C
8
D
5

57 △ABC has integer sides x, y, z such that xz = 12. How many such triangles are possible?

A
8
B
6
C
9
D
12

58 If the measure of the angles of a triangle are in the ratio 1 : 2 : 3 and if the length of the smallest side of the triangle is 10 cm, then the length of the longest side is:

A
20 cm
B
25 cm
C
30 cm
D
35 cm

59 A circle of radius 5 cm has chord RS at a distance of 3 unit's from it. Chord PQ intersects with chord RS at T such that TS = 1/3 of RT. Find minimum value of PQ:

A
6√3
B
4√3
C
8√3
D
2√3

60 Two mutually perpendicular chords AB and CD intersect at P. AP = 4, PB = 6, CP = 3. Find radius of the circle:

A
31.25($$\frac{1}{2}$$)
B
37.5($$\frac{1}{2}$$)
C
26($$\frac{1}{2}$$)
D
52($$\frac{1}{2}$$)