Q.315. Geometry

Question 315.
Find the angle α in the following figure.

Answer 315.

Refer to the figure (link below)

OD is parallel to BC

=> ∠ DOF = ∠ BCO = C/2 [corresponding angles] ... (1)

AD and AE are tangents to the incircle from A

=> AD = AE

=> Δ ADE is isosceles

and ∠ ADE = ∠ AED = (1/2) (π - A) = π/2 - A/2

=> ∠ ODF = π/2 - (π/2 - A/2) = A/2 ... (2)

α is an external angle of Δ DOF

=> α

= sum of the opposite internal angles

= ∠ DOF + ∠ ODF

= C/2 + A/2 ... [From (1) and (2)]

= π/2 - B/2

= 45°.

Link to YA!