MCQ
In the given figure, three circles with centres A, B, C, respectively, touch each other externally. If AB = 5cm, BC = 7cm and CA = 6cm, the radius of the circle with centre A is:
- A1.5cm
- ✓2cm
- C2.5cm
- D3cm
✓
Answer
Correct option: B.
2cm
Let the radii of the circle with centres A, B and C be x, y, and z respectively.
We know that radii of the same circle are equal.
x + y = 5
y + z = 7
z + x = 6
Adding the three equation, we get
2(x + y + z) = 18
⇒ x + y + z = 9
⇒ x = 2
So, the radius of the circle with centre A is 2cm.
We know that radii of the same circle are equal.
x + y = 5
y + z = 7
z + x = 6
Adding the three equation, we get
2(x + y + z) = 18
⇒ x + y + z = 9
⇒ x = 2
So, the radius of the circle with centre A is 2cm.
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