Question

In the following figure, $O$ is the center of circle. If $AB=6cm$ and $AC=5cm$ then the product of $AO$ and $AX$ is

• A. $15$
• B. $20$
• C. $25$
• D. $30$

Answer 1

The correct option is A $15$

$O$ is centre in given figure:

$AB=6cm,AC=5cm$

$\angle ACE=90$

$(\because AE=$ Diameter of circle)

$\angle A\times B=90$

$\angle ABX=\angle AEC$ (angle subtended by same are)

$\because △ABX\sim △AEC$ (By $AA$ similarity)

$\frac{AB}{AE}=\frac{BX}{EC}=\frac{AX}{AC}$

as ${}^{\prime }{O}^{\prime }$ is centre, $AE=2AO$

So,

$\frac{AB}{2AO}=\frac{BX}{EC}=\frac{AX}{AC}$

$2AO\times AX=AC\times AB$

$2\times AO\times AX=5\times 6$

$AO\times AX=5\times 3=15$

(Option $A$ is correct)