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Geometry - Triangles

Multiple Choice Questions

111.

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

equilateral
right
isosceles
obtuse

40 Views

112.

If G is the centroid of Δ ABC and Δ ABC = 48 cm², then the area of Δ BGC is

8 cm²
16 cm²
24 cm²
32 cm²

40 Views

113.

In a Δ ABC, ∠A = 90°, ∠C = 55°, What is the value of ∠BAD ?

60°
45°
55°
35°

31 Views

114.

Taking any three of the line segments out of segments of length 2 cm, 3 cm, 5 cm and 6 cm, the number of triangles that can be formed is

30 Views

115.

The radius of the circumcircle of a right angled triangle is 15 cm and the radius of its inscribed circle is 6 cm. Find the sides of the triangle.

30, 24, 25
24, 36, 30
30, 40, 41
18, 24, 30

33 Views

116.

In a ΔABC, ∠A : ∠B : ∠C = 2 : 3 : 4, A line CD is drawn || to AB, then ∠ACD is

80°
20°
40°
60°

28 Views

117.
ABC is an isosceles triangle with AB = AC. A circle through B touching AC at the middle point intersects AB at P. Then, AP : BP is

3 : 5

1 : 4

4 : 1

2 : 3

1 : 4

According to tangent-secant theorem:
"When a tangent and a secant are drawn from one single external point to a circle, square of the length of the tangent segment must be equal to the product of lengths of whole secant segment and the exterior portion of secant segment."
Now,
AD² = AP. AB
Given AB = AC and D is mid-point of AC.
$rightwards double arrow space space AD space equals space AC over 2 space equals space AB over 2 rightwards double arrow space space open parentheses AB over 2 close parentheses squared space equals space AP. space AB rightwards double arrow space space fraction numerator left parenthesis AB right parenthesis squared over denominator 4 end fraction space equals space AP. space AB rightwards double arrow space space space AB space equals space 4 AP Hence comma space AP space colon thin space AB space equals space 1 space colon space 4$

42 Views

118.

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