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, $$x=4$$

$$BD=4cm$$

Create a FREE account and get:

Download RRB Study Material PDF
45+ RRB previous papers with solutions PDF
300+ Online RRB Tests for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Venn Diagrams Questions CAT Arithmetic Questions CAT Time And Work Questions CAT Time Speed Distance Questions CAT Number Series Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Data Interpretation Questions CAT Maxima-Minima Questions CAT Data Interpretation Basics Questions CAT DI with connected data sets Questions CAT Selection With Condition Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Para Jumbles Questions CAT Odd One Out Questions CAT Vocabulary Questions CAT Verbal Ability Questions CAT Para Summary Questions

Follow us on

Boost your Prep!

Download App