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Geometry - Triangles

Multiple Choice Questions

11.

O is the circumcentre of $increment ABC.$ If AO = 8 cm, then the length of BO is

12 cm
3 cm
6 cm
6 cm

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12.
In $increment ABC comma space space AB space equals space straight a minus straight b comma space space AC space equals space square root of straight a squared plus straight b squared end root space space space and space space BC space equals space square root of 2 ab end root$ , then find angle B.

$60 degree$
$30 degree$
$90 degree$
$90 degree$

90 degree

AB = a - b
$BC space equals space square root of 2 ab end root$
AC = $square root of straight a squared plus straight b squared end root$
In $increment ABC comma$
$AB squared plus BC squared space equals space left parenthesis straight a minus straight b right parenthesis squared plus left parenthesis square root of 2 ab end root right parenthesis squared$

$equals straight a squared plus straight b squared minus 2 ab plus 2 ab equals straight a squared plus straight b squared space equals space AC squared$

$therefore$ $increment ABC$ is a right angled triangle.
$therefore$ $angle ABC space equals space 90 degree$

205 Views

13.

Possible measures of three angles of a triangle are

33°, 42°, 115°
40°, 70°, 80°
30°, 60°, 100°
30°, 60°, 100°

168 Views

14.

BD and CE are two medians of the triangle ABC. IF EO = 7 cm, then the length of CE is

28 cm
14 cm
21 cm
21 cm

340 Views

15.

Three median AD, BE and CF of $increment ABC$ intersect at G; are of $increment ABC$ is 36 sq cm. Then the area of $increment CGE$ is

12 sq cm
6 sq cm
9 sq cm
9 sq cm

230 Views

16.

The ratio between the vertical angle and a base angle of an isosceles triangle is 4 : 3. The value of any one base angle is

$18 degree$
$54 degree$
$72 degree$
$72 degree$

170 Views

17.

In $increment ABC comma space angle straight B space equals space 90 degree$ and $BC space equals space square root of 3 space AB$ . Find the measurement of $angle straight A.$