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In the figure shown, a circle is enclosed in trapezium ABCD touching all of its 4 sides, where AD = BC, AB = 10, CD = 16, find BC.

Jun 13, 2020

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In the figure shown, a circle is enclosed in trapezium ABCD touching all of its 4 sides, where AD = BC, AB = 10, CD = 16, find BC.

Hello Guest!

The contact radius at $$\overline{BC}$$ divides $$\overline{BC}$$ into $$\frac{\overline{DC}}{2}$$ and $$\frac{\overline{AB}}{2}$$.

$$\overline{BC}= \frac{\overline{CD}}{2}+ \frac{\overline{AB}}{2}$$

$$\overline{BC}= \frac{16}{2}+ \frac{10}{2}$$

$$\overline{BC}=13$$

!

Jun 13, 2020
edited by asinus  Jun 13, 2020
edited by asinus  Jun 13, 2020