Wait a Secant

Geometry Level 3

If $a=1,b=2,c=3,d=4$ , find $x$ .

Note: Figure is not to scale.

\frac{ 8}{3}

2

\frac{ 9}{4}

\frac{5}{2}

\frac{7}{3}

2 solutions

Hjalmar Orellana Soto
Jan 7, 2017

As $ABCD$ is cyclic, $\angle BAD \cong \angle BCE$ and $\angle ADC \cong \angle CBE$ , so $\bigtriangleup EAD \sim \bigtriangleup EBC$ , so we have: $\frac{\overline{EC}}{2}=\frac{x+1}{4}\Rightarrow \overline{EC}=\frac{x+1}{2}$ $\frac{x}{2}=\frac{\frac{x+1}{2}+3}{4} \Rightarrow 4x=x+7 \Rightarrow x\approx 2,33$

Ahmad Saad
Feb 15, 2016

Wait a Secant

2 solutions

0 pending reports