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. 4.

Question

KnowledgeBoat · Accepted Answer

Draw DY parallel to BF. 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 = AC Hence, option 3 is the correct option.

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. 4.

Mid-point Theorem

Related Questions

In the adjoining figure, AD = BD and DE || BC. If AC = 6 cm and DE = 4 cm, then the length of BC is :
4 cm
5 cm
6 cm
8 cm

In the given figure, BP and CQ are two medians of the △ABC. If BC = 12 cm, the length of QP =
4 cm
6 cm
8 cm
10 cm

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. 4.

Mid-point Theorem

Related Questions

In the adjoining figure, AD = BD and DE || BC. If AC = 6 cm and DE = 4 cm, then the length of BC is :4 cm5 cm6 cm8 cm

In the given figure, BP and CQ are two medians of the △ABC. If BC = 12 cm, the length of QP =4 cm6 cm8 cm10 cm

In the adjoining figure, AD = BD and DE || BC. If AC = 6 cm and DE = 4 cm, then the length of BC is :
4 cm
5 cm
6 cm
8 cm

In the given figure, BP and CQ are two medians of the △ABC. If BC = 12 cm, the length of QP =
4 cm
6 cm
8 cm
10 cm