Solve this:
Q. The line AB is 6 m in length and is tangent to the inner one of the two concentric circle at point C. It is known that the radii of the two circle are integers. The radius of the other circle.
(1) 5 m
(2) 4 m
(3) 6 m
(4) 3 m
Dear student
Say, radius of the inner circle = OC = r and radius of the larger circle = OB = R
And, AC = CB = AB/2 =3
Now, triangle OCB is a right-angled triangle with angle OCB = 90 degrees
Hence, OC, CB, and CB forms a Pythagorean triplet.
Hence, (r, 3, R) is a Pythagorean triplet in which both r and R are integers.
Now, there is only one integral Pythagorean triplet of which 3 is a part, which is (3, 4, 5)
Hence, R must be 5.
Regards
Say, radius of the inner circle = OC = r and radius of the larger circle = OB = R
And, AC = CB = AB/2 =3
Now, triangle OCB is a right-angled triangle with angle OCB = 90 degrees
Hence, OC, CB, and CB forms a Pythagorean triplet.
Hence, (r, 3, R) is a Pythagorean triplet in which both r and R are integers.
Now, there is only one integral Pythagorean triplet of which 3 is a part, which is (3, 4, 5)
Hence, R must be 5.
Regards