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In ∆ABC, AD is the bisector of ∠A meeting BC at D, CF ⊥ AB and E is the mid-point of AC. Then median of the triangle is
a. AD
b. BE
c. FC
d. DE

Solution:

Given, ABC is a triangle.

In ∆ABC, AD is the bisector of ∠A meeting BC at D, CF ⊥ AB and E is the mid-point of AC. Then median of the triangle is: a. AD, b. BE, c. FC, d. DE

AD is the bisector of ∠A meeting BC at D.

E is the midpoint of AC

Also, CF ⊥ AB

We have to find the median of the triangle.

Since E is the midpoint of AC,

AE = EC

The median of a triangle refers to a line segment joining a vertex of the triangle to the midpoint of the opposite side, thus bisecting that side.

From the figure,

The median BE touching the side bisects AC

So, AE = EC

Therefore, the median of the triangle is BE.

✦ Try This: In ∆ABC, if ∠A = 80°, and ∠B = 60°, then the exterior angle formed by producing BC is equal to

NCERT Exemplar Class 7 Maths Chapter 6 Problem 28

In ∆ABC, AD is the bisector of ∠A meeting BC at D, CF ⊥ AB and E is the mid-point of AC. Then median of the triangle is: a. AD, b. BE, c. FC, d. DE

Summary:

In ∆ABC, AD is the bisector of ∠A meeting BC at D, CF ⊥ AB and E is the mid-point of AC. Then, the median of the triangle is BE

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