Question

pls answer correctly....​

Answer 1

ANSWER:

a) 1/x + 1/y = 1/z

STEP-BY-STEP EXPLANATION:

Given that PA, QB and RC each is perpendicular to AC such thay PA = x, RC = y, QB = z, AB = a and BC = b.

We need to find out the correct value from the given options.

Now,

In ∆CAP and ∆CBQ

∠CAP = ∠CBQ (both 90°)

∠ACP = ∠BCQ (common angle C)

∆CAP ~ ∆CBQ

→ BQ/AP = BC/AC

Substitute the values,

→ z/x = b/AC ---------- (eq 1)

Similarly, In ∆ACR and ∆ABQ

∠ACR = ∠ABQ (both 90°)

∠RAC = ∠QAB (common angle A)

∆ACR ~ ∆ABQ

→ BQ/CR = AB/AC

Substitute the values,

→ z/y = a/AC ---------- (eq 2)

Now, add (eq 1) and (eq 2)

→ z/x + z/y = b/AC + a/AC

Take commons from them,

→ z(1/x + 1/y) = 1/AC (b + a)

→ z (1/x + 1/y) = 1/AC (b + a)

Where b is BC and a is AB. So, we can write (b + a) as AC.

→ z (1/x + 1/y) = 1/AC × AC

→ z (1/x + 1/y) = 1

→ 1/x + 1/y = 1/z

Therefore, correct option is option a) 1/x + 1/y = 1/z.