Question 78

Let $$\triangle$$ be the area of the circumcircle of a right angled triangle ABC with $$\angle B$$ = 90°. Let $$\triangle_1 and \triangle_2$$ be areas of the two circle with diameters BC and BA respectively. Then

Solution

Let say ,a be the length of the side conjugate to the right angle .

so,length of the diameter of the circle is

$$=√2a$$.

so,radius$$=(√2/2)a$$.

so,$$∆=πa^2/2$$.

Now,∆1=∆2=

$$π(a/2)^2=πa^2/4.$$

So,∆1+∆2=$$πa^2/2.$$

So,∆=∆1+∆2.

C is correct choice.

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