The medians of the line of triangle ABC meet at point O. A straight line is drawn through point O, parallel to side AC

| March 3, 2021 | education

The medians of the line of triangle ABC meet at point O. A straight line is drawn through point O, parallel to side AC and intersecting sides AB and BC at points E and F, respectively. Find EF if the AC side is 15 cm.

Let us prove that triangles ACD and ECO are similar.

The angle C is common for the triangles. Since, according to the condition, the segment EF is parallel to the segment AB, then the angle ADC = EOC as the corresponding angles at the intersection of parallel straight lines EF and AB secant CD. Then the triangles ASD and ECO are similar in two angles.

By the property of the medians of the triangle, they are divided at the point O in the ratio 2/1.

Then OS = 2 * CD / 3.

OC / CD = 2/3 = K.

Then EO / AD = 2/3.

EO = 2 * AD / 3.

AD = AB / 2 = 15/2 = 7.5 cm.

EO = 2 * 7.5 / 3 = 5 cm.

EO is the median of the CEF triangle, then EF = 2 * EO = 2 * 5 = 10 cm.

Answer: The length of the segment EF is 10 cm.



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