In ΔABC, ADBC and AD2=BD×CD. Prove that BAC=90.

A B D C


Answer:


Step by Step Explanation:
  1. Given:
    ADBC and AD2=BD×CD

    Here, we have to find the value of BAC.
  2. Now, we have: AD2=BD×CDBDAD=ADCD

    Now, in ΔDBA and ΔDAC, we have

    A B D C 2 1 BDA=ADC=90 and BDAD=ADCD  ΔDBAΔDAC          [By SAS-similarity] As the corresponding angles of similar triangles are equal. So,   B=2 and 1=C  1+2=B+C  A=B+C          [where, A=1+2]  2A=A+B+C          [Adding A on both sides. ]  2A=A+B+C=180          [Sum of angles of a triangle is of 180.]  A=BAC=90.

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