Question

explain the solutions of this question ❓ please​

Answer 1

Step-by-step explanation:

AB =h

PQ = 2h

BM = x

QM = y

According to the question if ∠AMB = θ then ∠PMQ = 90 - θ

Applying cot θ in ΔABM,

cot θ  = BM/AB = x/h

similarly applying tan (90 - θ) in ΔPQM,

tan (90 - θ) = PQ/MQ = 2h/y

we know that,

tan (90 - θ) = cot θ  

∴ 2h / y = x / h

2h² = xy

(dividing L.H.S and R.H.S by 2)

h² = xy /2

hence proved