Question

In the given figure, O is equidistant from the sides AC and AB. Then the value of x - 3 is ___.

Answer 1

$\text{In}\Delta AOC\text{and}\Delta AOB,OC=OB\text{(Given)}\angle OBC=\angle OCA\text{(Both angles are right angles)}\text{And}AO\text{is common side}.\text{Hence,}\Delta AOC\cong \Delta AOB\text{(RHS congruence)}\therefore \angle CAO=\angle BAO\text{(CPCT)}\Rightarrow 2x+24=30\Rightarrow x=3\Rightarrow x-3=0$