Question

Let ABCD be a square. M, N, R are the points on AB, BC and CD respectively such that AM = BN = CR. If ∠MNR is a right angle, then ∠MRN is equal to 

(a) 30° 

(b) 45° 

(c) 60° 

(d) 75°

Answer 1

(b) 45°.

Let each side of the square = x units 

Let AM = BN = CR = y units 

⇒ MB = CN = DR 

= (x – y) units 

In ∆s MBN and NCR 

MB = NC = (x – y) 

BN = CR = y 

∠MBN = ∠NCR = 90° 

⇒ ∆MBN ≅ ∆NCR

⇒ MN = NR 

Given, ∠MNR = 90° 

⇒ DMNR is an isosceles right angled triangle. 

⇒ ∠MRN = ∠NMR = 45°.