Question

Suppose a circle passes through $(2,2)$ and $(9,9)$ and touches the $x-$axis at $P$. If $o$ is the origin, then $OP=$

• A. $4$
• B. $5$
• C. $6$
• D. $9$

Answer 1

Answer: (C)

$6$

From the above figure, we can say that,

r = $\sqrt{(h-h{)}^2+(k-0{)}^2}=k$

Also, CA = CB = r

$\to C{A}^2=C{B}^2$

$\to (h-2{)}^2+(k-2{)}^2=(h-9{)}^2+(k-9{)}^2$

Solving we get, $(h+k)=11$

Again, CA = r

$\to C{A}^2=r^2$

$(h-2{)}^2+(k-2{)}^2=k^2$

Solving we get, h = $\pm 6$

$P\equiv (\pm 6,0)$

So, OP = 6.

Hence, (C) is the correct answer.