Question

Dis a point on the side BC of a triangle
ABC such that Z ADC = Z BAC. Show
that CAP=CB.CD​

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)

AB=CB=CA

AD=CA=CD

consider = CB = CA

_ _

CA CD

∴ CB x CD = CA²