Question

Point D is chosen on the side AC of triangle ABC so that DC = AB, Points M and N are the midpoints of the segments AD and BC, respectively. Angle NMC= α°. Find angle BAC=?

Answer 1

Step-by-step explanation:

In ΔADC and ΔBAC,

∠ADC = ∠BAC (Given)

∠ACD = ∠BCA (Common angle)

∴ ΔADC ~ ΔBAC (By AA similarity criterion)

We know that corresponding sides of similar triangles are in proportion.

∴ CA/CB =CD/CA

⇒ CA2 = CB.CD. 

An alternate method:

Given in ΔABC, ∠ADC = ∠BAC

Consider ΔBAC and ΔADC

∠ADC = ∠BAC (Given)

∠C = ∠C (Common angle)

∴ ΔBAC ~ ΔADC (AA similarity criterion)

⇒ 

∴ CB x CD = ca2