# The height of the isosceles trapezoid drawn from the vertex C divides the base AD

The height of the isosceles trapezoid drawn from the vertex C divides the base AD into segments of length 2 and 9. Find the length of the base BC.

Take an isosceles trapezoid ABCD with bases AD and BC, | AD | > | BC |, and sides AB and CD, | AB | = | CD |.

In isosceles trapezoid ABCD, draw the heights BM and CN from vertices B and C to the lower base AD. By the condition of the problem:

| AN | = 9;

| ND | = 2;

Based on the properties of an isosceles trapezoid:

| AM | = | ND | = 2;

| BC | = | MN |;

Notice, that:

| AM | + | MN | = | AN |;

| MN | = | AN | – | AM | = | AN | – | ND |;

| MN | = 9 – 2 = 7;

As a result, we get for the base BC:

| BC | = | MN | = 7;

Answer: BC base length is 7

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