Question 60

In the circle above, chord $$\overline{AB}$$ is extended to meet the tangent $$\overline{DE}$$ at D. If $$\overline{AB} = 5$$ cm and $$\overline{DE} = 6$$ cm,find the length of $$\overline{BD}$$.

Solution

given, $$AB=5cm$$ and $$DE=6cm$$

Let $$BD=xcm$$

therefore, $$AD=(x+5)cm$$

by tangent theorem

$$DE^2$$ = $$AD$$ * $$BD$$

$$6^2$$ = $$(x+5)$$ * $$x$$

$$36=x^2+5x$$

$$x^2+5x-36=0$$

$$\left(x-4\right)\cdot\left(x+9\right)=0$$

$$x=4$$ and $$x=-9$$ (not possible)

Hence, $$x=4$$

$$BD=4cm$$

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