Question

The length of the tangent from an external point P to a circle of radius 5 cm is 10 cm. The distance of the point from the centre of the circle is
(a) 8 cm
(b) $\sqrt{104}$ cm
(c) 12 cm
(d) $\sqrt{125}$ cm

Answer 1

We know that the radius and tangent are perperpendular at their point of contact
In right triangle PTO
By using Pythagoras theorem, we have
PO² = OT² + TP²
⇒ PO² = 5² + 10²
⇒ PO² = 25 + 100
⇒ PO² = 125
⇒ PO = $\sqrt{125}$ cm
Hence, the correct answer is option (d).