In Fig. 5, l and

Proof:

Let l be XY and m Be X’Y’.

From fig-

∠XDE + ∠X'ED = 180°

[∵ Sum of consecutive interior angles is 180°.]

(1/2) ∠XDE + (1/2) ∠X'ED = 90°

⇒ ∠1 + ∠2 = 90° ...(1)

[∵ OD is equally inclined at the tangents]

In Δ ODE,

(∠1 + ∠2) + ∠3 = 180°

[∵ Angle-sum-property of a Δ]

⇒ 90° + ∠3 = 180° [from (1)]

⇒ ∠3 = 90°

∴ ∠ DOE = 90° …proved