If D is the diameter of the larger circle and d is the diameter of the small circle then D+d=?
(A) a+b (B) 2(a+b) (C) √2(a+b) (D) 2√ab
NOTE: I'm assuming that there is a right angled triangle whose sides are tangents to the smaller circle.
Ans is a+b
Solution: Let the triangle be P
|
y x
|
Q----z------ R
where P,Q and R are vertices and x, y and z are points of intersection with inner circle.
Now, it is clear that sides of triangle are tangent to the inner circle.
So, as tangents from an external point are equal,
In smaller cicle, let the centre be O
As tangents are perpendicular to radius,
D + d = PY + RZ + QY + QZ = PQ + QR
Hence, D + d = a + b
Ans is a+b
Solution: Let the triangle be P
|
y x
|
Q----z------ R
where P,Q and R are vertices and x, y and z are points of intersection with inner circle.
Now, it is clear that sides of triangle are tangent to the inner circle.
So, as tangents from an external point are equal,
- PY = PX
- QY = QZ
- RX = RZ
In smaller cicle, let the centre be O
As tangents are perpendicular to radius,
- OY | QY
- OZ | QZ
D + d = PY + RZ + QY + QZ = PQ + QR
Hence, D + d = a + b