Question

AB, CD are the chords of a circle with center O.
The chords interected E. AE=4cm, DE=3cm, EC=8cm and EB=x cm, find x, OE and the area of the circle.

Answer 1

According to the theorem:

$4\times x=8\times 3$

(Product of segments cut on two chords are equal)

$\Rightarrow x=6$

In $△BEC$

$B{E}^2+E{C}^2=B{C}^2$

$\Rightarrow 36+64=(2r^2{)}^2$

$\Rightarrow 4r^2=100$

$\Rightarrow r^2=25$

$\Rightarrow r=5cm$

Circle $=\pi r^2$

$=\pi \left(5^2\right)$

$=25\pi$