Tangent drawn from a point Y, touches the circle at X. O is the centre of this circle. If OY = 50 cm and XY = 40 cm, then what will be thee radius of this circle?

30 cm

By the problem, OY is the hypotenuse and OX is one of the sides of a right angled triangle OXY.

Use pythagoras theorem to find length of OX, which is the radius of the circle.

= \( {OY }^{2 } \) = \( {OX }^{2 } \) + \( {XY }^{2 } \)

= \( {OX }^{2 } \) = \( {OY }^{2 } \) - \( {XY }^{2 } \)

= \( {OX }^{2 } \) = \( {50 }^{2 } \) - \( {40 }^{2 } \)

= \( {OX }^{2 } \) = 2500 - 1600 = 900

= OX = 30 cm

Therefore, the radius of the circle is 30 cm.