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Mathematics

In △ABC, E is the mid-point of the median AD. BE is joined and produced to meet AC at F. Then, AF = ….AC.

  1. 3

  2. 2

  3. 13\dfrac{1}{3}

  4. 12\dfrac{1}{2}

Mid-point Theorem

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Answer

Draw DY parallel to BF.

In △ABC, E is the mid-point of the median AD. BE is joined and produced to meet AC at F. Then, AF = ....AC. R.S. Aggarwal Mathematics Solutions ICSE Class 9.

Since, BF || DY so, EF || DY

By converse of mid-point theorem,

A line drawn through the midpoint of one side of a triangle, and parallel to another side, will bisect the third side.

In △ADY,

Since, E is the mid-point of AD and EF || DY

⇒ F is the mid-point of AY.

∴ AF = FY

Given,

AD is the median.

In △BCF,

Since, D is the mid-point of BC and BF || DY

⇒ Y is the mid-point of FC.

∴ FY = CY

⇒ AF = FY = CY

From figure,

AC = AF + FY + CY = AF + AF + AF = 3 AF

⇒ AF = 13\dfrac{1}{3} AC

Hence, option 3 is the correct option.

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