Question 9.

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.