Math, asked by asifanu9554, 5 months ago

D is a point on the side BC of a triangle ABC such that ∠ ADC = ∠ BAC. Show that CA2 = CB.CD PLzzz give full expln

Answers

Answered by prabhas24480
0

\huge\bold{\gray{\sf{Answer:}}}

\bold{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)

\frac{AB}{AD} = \frac{CB}{CA} = \frac{CA}{CD}

Consider, \frac{CB}{CA} = \frac{CA}{CD}

Hope This Helps :)

∴ CB x CD = CA²

Attachments:
Answered by BrainlyFlash156
0

\huge\underbrace\mathfrak \red{ANSWER }

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)

\frac{AB}{AD} = \frac{CB}{CA} = \frac{CA}{CD}

Consider, \frac{CB}{CA} = \frac{CA}{CD}

Hope This Helps :)

∴ CB x CD = CA²

HOPE SO IT WILL HELP......

PLEASE MARK IT AS BRAINLIST.....

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