Question

In triangle ABC, mid points of BC, CA and AB are D, E and F

respectively. FE intersects AD at O. AD = 6cm. Find the length of AO.​

Answer 1

In triangle ABC , as F is midpoint of AB and D is midpoint of BC , we apply the theorem:-

the line segment joining the midpoints of two side of a triangle is parallel to the third side and equal to half of it , we get

=> FD = ½ AC AND FD || AC

also , it is given that E is the midpoint of AC

=> AR = ½AC

from adove two equation , we get , AE = FD

In triangle FOD AND TRIANGLE EOA ,

< FOD= < EOA ( OPPOSITE ANGLE)

FDO = EAO ( AIA AS FD || AE )

ALSO OFD = OEA ( AIA AS FD || AE )

=> triangle FOD = triangle EOA

AO =OD

=> AO = ½AD

=> AO = ½ × 6 = 3 vm

The length of AO is 3 cm

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