Geometry problem with circumference

Question

Could someone explain me how to demonstrate the following problem ?

(I had to translate it so sorry for any grammatical mistakes as english isn't my first language)

From a point C outside a circumference draw a tangent CA and a secant that intersect the circumference in B and D with CB larger than CD. From a point E on the secant with CE lesser than CD draw the parallel to AB that intersects the tangent in F. Demonstrate that $\angleCAD = \angleDEF$ and that the quadrilateral ADEF can be inscribed.

Thank you in advance

Should it be $\angle CAD=\angle CEF$? – CY Aries Apr 17 '18 at 06:10 — CY Aries, Apr 17 '18 at 06:10

score 0 · Answer 1 · answered Apr 17 '18 at 06:46

$\angle CAD=\angle DBA$ (angle in alternate segment)

$\angle CEF=\angle DBA$ (corresponding angles of parallel lines)

So, $\angle CAD=\angle CEF$.

$ADEF$ is a cyclic quadrilateral is a consequence of $\angle CAD=\angle CEF$. (exterior angle is equal to interior opposite angle)

Geometry problem with circumference

1 Answers1