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D is a point on the …

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

    • Posted by Narinder Singh Singh 5 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gaurav Seth 5 years, 4 months ago

    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

    1Thank You

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