Question

11.D is a point on the side of triangle ABC,such that angleADC=angleBAC.Show that CA^2=CB.CD

Answer 1

Question is Incomplete,Complete Question is below.

D is a point on the side BC of a triangle ABC such that angle ADC = angle BAC Show that CA square=CB .CD

Answer:

The Proof is given below.

Explanation:

Given:

In ΔABC,

∠ADC = ∠BAC

To Show:

`CA^(2)=CB.CD`

Proof:

In ΔBAC and ΔADC

∠ADC = ∠BAC ............................Given

∠C = ∠C .....................................Reflexive Property

∴ ΔBAC ~ ΔADC .................... A-A similarity test

If two triangles are similar then their sides are in proportion.

`(BA)/(AD) =(BC)/(AC) =(AC)/(CD)\ \textrm{corresponding sides of similar triangles are in proportion}\\`

`(BC)/(CA) =(CA)/(CD)\\\\\therefore CA.CA=CB.CD\\\\\therefore CA^(2)=CB.CD`..........Proved