XY and XZ are tangents to a circle, ST is another tangent

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XY and XZ are tangents to a circle, ST is another tangent to the circle at the point R on the circle, which intersects XY and XZ at S and T respectively. If XY = 15 cm and TX = 9 cm, then RT is

1. 4.5 cm
2. 7.5 cm
3. 6 cm
4. 3 cm

Correct Option: C

As per the given in question , we draw a figure of a circle in which XY and XZ are tangents

We can say that the tangents drawn from an exterior point to a circle are equal.
∴ XY = XZ = 15 cm.
∴ TZ = XZ – TX
TZ = 15 – 9 = 6 cm
Argain, TR = TZ = 6 cm