Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

E is the mid-point of the median AD of a \( \Large \triangle ABC \). If BE is extended it meets the side AC at F, then CF is equal to

A) \( \frac{AC}{3} \)
B) \( \frac{2 AC}{3} \)
C) \( \frac{AC}{2} \)
D) None of these

Correct Answer:


B) \( \frac{2 AC}{3} \)

Description for Correct answer:
Draw line segment DG parallel to BF

Then in, \( \Large \triangle ADG, \)

\( \Large EF \parallel DG \)

and AE = ED

\( \Large \therefore AF = GC \) ...(i)

Similarly, in \( \Large \triangle BCF, \)

\( \Large DG \parallel BF \)

and BD = DC

\( \Large \therefore FG = GC \) ...(ii)

From Eqs. (i) and (ii),

\( \Large CF = \frac{2}{3}AC \)

Part of solved Geometry questions and answers : >> Elementary Mathematics >> Geometry

Comments

Similar Questions

1). Consider the following statements
I. If G is the centroid of \( \Large \triangle ABC \), then GA = GB = GC.
II. If H is the orthocentre of \( \Large \triangle ABC \), then HA = HB = HC.
Which of the statements given above is/are correct?

A). Only I

B). Only II

C). Both I and Il

D). Neither I nor ll

2). The three sides of a triangle are 15, 25 and x units. Which one of the following is correct?

A). 10 < x < 40

B). \( \Large 10 \le x \le 40 \)

C). \( \Large 10 \le x < 40 \)

D). \( \Large 10 < x \le 40 \)

3). If AD is the internal angle bisector of \( \Large \triangle ABC \) with AB = 3 cm and AC = 1 cm, then what is BD : BC equal to?

A). 1: 3

B). 1: 4

C). 2 : 3

D). 3: 4

4). In a \( \Large \triangle ABC \), if \( \Large \angle A \) = 115 degree, \( \Large \angle C \) = 20 degree and D is a point on BC such that \( \Large AD \perp BC \) and BD = 7 cm, then AD is of length

A). 15 cm

B). 5 cm

C). 7 cm

D). 10 cm

5). In \( \Large \triangle ABC \), \( \Large DE \parallel BC \), where DE intersects AB and AC at the points D and E, respectively. If AD = 6 cm, DB = 12x - 6 cm, AE = 2x cm and CE = 16 - 2x cm, then the value of x is

A). 6 cm

B). 4 cm

C). 2 cm

D). 8 cm

6). In \( \Large \triangle ABC \), D and E are points on sides AB and AC, such that \( \Large DE \parallel BC \). If AD = x, DB = x - 2, AE = x + 2 and EC = x - 1, then the value of x is

A). 4

B). 2

C). 1

D). 8

7). In \( \Large \triangle ABC \), AB = AC and D is a point on AB, such that AD = DC = BC. Then \( \Large \angle BAC \), is

A). \( \Large 40 ^{\circ} \)

B). \( \Large 45 ^{\circ} \)

C). \( \Large 30 ^{\circ} \)

D). \( \Large 36 ^{\circ} \)

8). In a \( \Large \triangle ABC \), \( \Large \angle A \) : \( \Large \angle B \) : \( \Large \angle C \) = 2 : 3 : 4. A line CD drawn parallel to AB, then \( \Large \angle ACD \) is

A). \( \Large 80 ^{\circ} \)

B). \( \Large 20 ^{\circ} \)

C). \( \Large 40 ^{\circ} \)

D). \( \Large 60 ^{\circ} \)

9). The mid-points of AB and AC of a \( \Large \triangle ABC \) are respectively X and Y. If BC + XY = 12 units, then the value of BC - XY is

A). 6

B). 8

C). 4

D). 12

10). In the figure given below, \( \Large \angle ABC \) = \( \Large \angle AED \) = \( \Large 90 ^{\circ} \)

Consider the following statements
I. ABC and ADE are similar triangles.
II. The four points B, C, E and D may lie on a circle.
Which of the above statements is/are correct?

A). Only I

B). Only II

C). Both I and ll

D). Neither I nor ll