Question

In the given figure, ∠ABC = ∠AED = 90°. Consider the following statements:

I. ABC and ADE are similar triangles. 

II. The four points B, C, E and D may lie on a circle. 

(a) Only I 

(b) Only II 

(c) Both I and II 

(d) Neither I nor II

Answer 1

(c) Both I and II 

In Δs ABC and ∆AED 

∠ABC = ∠AED = 90° 

∠A = ∠A 

∴ ∠ABC ~ ∠AED (AA similarly) 

Also, ∠DEC = 180° – 90° = 90°. 

In quadrilateral EDBC 

∠E + ∠D + ∠C + ∠B = 360° ⇒ ∠C + ∠D = 180°

∴ Opposite angles are supplementary, EDBC is cylic quadrilateral.