In above figure a right angled triangle is given with hypotenuse =h, base =b, height =p, According to Pythagoras theorem for above right angled triangle h2 =b2+p2.
Now see the figure given below a circle of radius is inscribed in a quarter circle of radius X
Question: using the information given in the passage above , find the relation between x and r?
A) (√2 + 1)r = x
B) (√2-1)=x
C) 2r = X
D) 2√2=X
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Given :- A circle of radius r is inscribed in a quarter circle of radius X .
To Find :- The relation between X and r ?
A) (√2 + 1)r = X
B) (√2-1) = X
C) 2r = X
D) 2√2 = X
Answer :-
from image we can see that,
- AOCD is a square .
- AO = OC = OM = r .
- OD = Diagonal of square = √2r .
- DM = X (radius of quadrant .)
so,
→ DO + OM = DM
→ √2r + r = X
→ (√2 + 1)r = X (A) (Ans.)
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