Question

in the figure ABCDE is a regular pentagon. Prove that ABCE is a cyclic quadrilateral

see the attachment for the figure. please answer correctly. ​

Answer 1

Join AC and BE In ∆s ABC and BCE,

we have AB = CE (sides of a regular pentagon)

∠ABC = ∠BCE (angles of a regular pentagon)

BC is common

∴ ∆ ABC ≅ ∆ BCE (SAS)

⇒ ∠BAC = ∠BEC (c.p.c.t.)

⇒ A, B, C, D are cyclic (Since ∠BAC and ∠BDC are angles subtended by BC on the same side of it.)

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