Question

In the given figure, PM : MQ = 5 : 6. The values of a and b are respectively

• A. 6 and 5
• B. 5 and 6
• C. 6 and 6
• D. 5 and 5

Answer 1

The correct option is B 5 and 6

Given: PM : MQ = 5 : 6


Here, ray PX and QY are constructed such that PX || QY and PQ is transversal.

In $\Delta P{P}_{a}Mand\Delta Q{Q}_{b}M$,
$\angle MP{P}_a=\angle MQ{Q}_b$
(Alternate interior angles)
$\angle M{P}_{a}P=\angle M{Q}_{b}Q$
(Alternate interior angles)
$\Delta P{P}_{a}M\sim \Delta Q{Q}_{b}M$
(By AA similarly)

$\Rightarrow \frac{P{P}_a}{Q{Q}_b}=\frac{PM}{QM}=\frac{5}{6}$

$\Rightarrow P{P}_a:Q{Q}_b=5:6$

$\Rightarrow a=5andb=6$

Hence, the correct answer is option b.