In the given figure, TB is a chord which passes through the centre of the circle. PT is a tangent to the circle at the point T on the circle. If PT = 10 cm, PA = 5 cm and AB = x cm, then the radius of the circle is:

In the given figure, TB is a chord which passes through the centre of the circle. PT is a tangent to the circle at the point T on the circle. If PT = 10 cm, PA = 5 cm and AB = x cm, then the radius of the circle is:

Answer: Option A

Solution

Answer: Option A

Solution:

PA × PB = PT²
5(5 + x) = 100
x = 15
In right angle triangle PTB,
TB² = 20² - 10²
TB² = $$10\sqrt{3}$$
So, OT $$=\frac{10\sqrt{3}}{2}=5\sqrt{3}$$