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Geometry - Triangles

Multiple Choice Questions

41.

A point D is taken from the side BC of a right-angled triangle ABC, where AB is hypotenuse. Then

AB² + CD² = BC² + AD²
CD² + BD² = 2 AD²
AB² + AC² = 2AD²
AB² + AC² = 2AD²

540 Views

42.

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 sides AB and AC respectively of ΔABC. If AP = a cm, AQ = b cm and ∠BAD = 15°, sin 75° =

$fraction numerator 2 straight b over denominator square root of 3 space straight a end fraction$
$fraction numerator straight a over denominator 2 straight b end fraction$
$fraction numerator square root of 3 straight a over denominator 2 straight b end fraction$
$fraction numerator square root of 3 straight a over denominator 2 straight b end fraction$

974 Views

43.
D and E are two points on the sides AC and BC respectively of Δ ABC such that DE = 18 cm, CE = 5 cm and ∠DEC = 90°, If tan ∠ABC = 3.6, then AC : CD =

BC : 2 CE

2 CE : BC

2 BC : CE

2 BC : CE

2 BC : CE

angle DEC space equals space 90 degree space space DE space equals space 18 space cm space space CE space equals space 5 space cm

therefore space space tan space straight C space equals space DE over CE space equals space 18 over 5 space equals space 3.6 space space tan space angle ABC space equals space 3.6 therefore space space space space angle straight C space equals space angle straight B therefore space space space space AC space equals space AB

angle straight C space plus space angle straight D space equals space 90 degree rightwards double arrow space space 2 angle straight C space plus space 2 angle straight D space equals space 180 degree space rightwards double arrow space space space angle straight C space plus space angle straight A space plus space angle straight B space equals space 180 degree

rightwards double arrow space 2 straight C space plus space angle straight A space equals space 180 degree therefore space space space angle straight A space equals space 2 angle straight D therefore space space AC over CB space equals space fraction numerator 2 CD over denominator CE end fraction

1793 Views

44.

D is a point on the side BC of a triangle ABC such that $AD space perpendicular space BC$ . E is a point on AD for which AE : ED = 5 : 1. If $angle BAD space equals space 30 degree$ and then $tan left parenthesis angle ACB right parenthesis space equals space 6 space tan space space left parenthesis angle DBE right parenthesis comma$ then $angle ACB space equals$

30°
45°
60°
40°

308 Views

45.

In ΔABC, P and Q are the middle points of the sides AB and AC respectively. R is a point on the segment PQ such that PR : RQ = 1 : 2. If PR = 2cm, the BC =

4 cm
2 cm
12 cm
12 cm

229 Views

46.

The angles of a triangle are in Arithmetic Progression. The ratio of the least angle in degrees to the number of radians in the greatest angle is $60 thin space colon space straight pi$ . The angles in degrees are

30°, 60°, 90°
35°, 55°, 90°
40°, 50°, 90°
40°, 50°, 90°

225 Views

47.

If the incentre of an equilateral triangle lies inside the triangle and its radius is 3 cm, then the side of the equilateral triangle is

$9 square root of 3 space cm$
$6 square root of 3 space cm$
$3 square root of 3 space cm$
$3 square root of 3 space cm$

171 Views

48.

Suppose ΔABC be a right-angled triangle where $angle straight A space equals space 90 degree$ and $AD space perpendicular space BC.$ If Δ ABC = 40 cm², ΔACD = 10 cm² and $AC with bar on top space equals space 9 space cm comma$ then the length of BC is

12 cm
18 cm
4 cm
4 cm

164 Views

49.

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
$1 space colon space square root of 2 minus 1$
$1 space colon space square root of 2$
$1 space colon space square root of 2$

433 Views

50.

I is the incentre of a triangle ABC. If $angle ABC space equals space 65 degree$ and $angle ACB space equals space 55 degree comma$ then the value of $angle BIC$ is