In the adjoining figure, 2 circles with centres Y and Z touch each other externally at point A.

Another circle, with centre X, touches the other 2 circles internally at B and C. If XY = 6 cm, YZ = 9 cm and ZX = 7 cm, then find the radius of the circle with centre Y.

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Solution

The correct option is B 5
Let X, Y, Z be the radii of the circle, with centres at X, Y, Z respectively. YAZ, XYB, XZC are straight lines (Contact of circles)
XY = X - Y = 6..........(1)
YZ = X + Y = 9.......(2)
ZX = X - Z = 7...........(3)
(1) + (2) + (3)
2X = 22 $\Rightarrow X = 11, Z = 4$
The radius of the circle, centre X, is 11 cm.
The radius of the circle, centre Y, is 5 cm.
The radius of the circle, centre Z, is 4 cm.

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In the adjoining figure, 2 circles with centres Y and Z touch each other externally at point A. Another circle, with centre X, touches the other 2 circles internally at B and C. If XY = 6 cm, YZ = 9 cm and ZX = 7 cm, then find the radius of the circle with centre Y.

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