Since OA = 4 m and OB=3 m; AB = 5 m. OR bisects the chord into PC and QC.
Since AB = 5 m, we have $a + b = 5$ …(i) Also,
$4^2 - k^2 = a^2$. …(ii) and
$3^2 - k^2 = b^2$. …(iii)
Subtracting (iii) from (ii), we get:
$a^2 - b^2 = 7$…(iv)
Substituting (i) in (iv), we get
$a - b = 1.4$ …(v);
[$(a + b)(a - b) = 7$; ∴ $(a - b) = \frac{7}{5}$]
Solving (i) and (v), we obtain the value of $a = 3.2$ and $b = 1.8$
Hence, $k^2 = 5.76$
Moving on to the larger triangle
$\triangle POC$, we have $5^2 - k^2 = (x + a)^2$;
Substituting the previous values, we get: $(25 - 5.76) = (x + 3.2)^2$
$\sqrt{19.24} = (x + 3.2)$ or $x = 1.19$m
Similarly, solving for y using
$\triangle QOC$, we get $y = 2.59$m
Therefore, $PQ = 5 + 2.59 + 1.19 = 8.78$ ≈ $8.8$m
Hence, Option C is the correct answer.
