Question

Abc is a right angled triangle which is right angled at b and p is the mid-point of ac. prove that pb=pa=1/2ac

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:

Step-by-step explanation:

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]