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Question

In the given figure, ΔABC is an obtuse triangle, obtuse angled at B. If ADCB, then prove that AC2=AB2+BC2+2BC.BD
517307_572f95b97dc24968ad9f03c833a80455.png

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Solution

Given: ABC is obtuse triangle.
AB2=AD2+DB2(1)
AC2=AD2+DC2(2)

from (1) AD2=AB2DB2

AC2=AB2DB2+(DB+BC)2[BC=DB+BC]

AC2=AB2DB2+DB2+BC2+2BC×DB

AC2=AB2+BC2+2BC×DB (Proved)

1011777_517307_ans_009fc39ad12b4e86b0512e68640a4167.png

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