Question

ABC is a right angle triangle which is right angled at B and P is the midpoint of AC prove that BP = P A = half AC

Answer 1

ABC is a right triangle with <B = 90 deg; P is the midpoint of AC [Given]  

==> AP = PC = (1/2)AC ---- (1)  

So taking AC as diameter, constructing a circle,  

it will pass through the 3 vertices A, B & C  

Reason: PA = PC  

<B being 90 deg and AC being diameter, B will lie on the circle;  

since angle in a semi circle is 90 deg.  

==> PA = PB = PC [All are radii of the same circle] ---- (2)  

Hence from (1) & (2), PA = PB = (1/2)AC [Proved]

Answer 2

Answer:

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