Question 21

A point D is taken from the side BC of a right angled triangle ABC, where AB is hypotenuse. Then,

Solution

$$\triangle$$ ABC is a right angled triangle right angled at C

$$\Rightarrow$$ $$AB^{2} = AC^2+BC^2$$ ( From Pythagoras theorem )

$$\Rightarrow$$ $$AC^2 = AB^2-BC^2$$

From $$\triangle ACD$$, $$AD^2 = AC^2+CD^2$$

Substituting $$AC^2 = AB^2-BC^2$$ in above equation

$$AD^2 = AB^2-BC^2+CD^2$$

$$\Rightarrow$$ $$AB^{2}+CD^{2}=BC^{2}+AD^{2}$$

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