Question:
<p>If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is</p>
<p style="display:inline">(b, a)</p>
<p style="display:inline"><span class="math-tex">\(\left(\frac{a}{2}, \frac{b}{2}\right)\)</span></p>
<p style="display:inline"><span class="math-tex">\(\left(\frac{b}{2},-\frac{a}{2}\right)\)</span></p>
<p style="display:inline">(a, b)</p>
Step-by-Step Solution
Key Concept: The circumcenter of a right-angled triangle is the midpoint of its hypotenuse.
<html><body><p><img alt="" data-imgur-src="5PORusw.png" height="102" src="https://media-mycbseguide.s3.amazonaws.com/images/imgur/1623761521-7fqheg.jpg" width="141"/><br/>
Let O = (0, 0), A = (a, 0) and B = (0, b).<br/>
<span class="math-tex">$\Rightarrow$</span> <span class="math-tex">$\triangle$</span>OAB is a right angled triangle<br/>
<span class="math-tex">$\Rightarrow$</span> Centre = mid point of AB <span class="math-tex">$=\left(\frac{a}{2}, \frac{b}{2}\right)$</span></p></body></html>
Correct Answer: B