Question

In a triangle ABC, AD is perpendicular to BC, if AD^2 = BD x DC. Prove that angle BAC 90°

Answer 1

Answer:

See this the answer is simple.

Step-by-step explanation:

From triangle ABC and ADC;

AD is common;

BD=DC=AD.

angle ADB=angle ADC.

therefore both the triangles are congruent.

therefore angle ABD=angleACD.AB=BC.

NOTE:-We find here that the Triangles ABD and ADC are iscoscelese triangles.

so angles:

ABC,BAD,CAD,ACD are equal.

now by changing others with angle BAD we get an equation:

4angle BAD=180degrees. (Just adding all the angles.)

so by calculating we get angle BAD=45 degrees.

now angle BAC=2angleBAD

so angle BAC=90 degrees.

There is no need of using the given equation from the question.