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 & explanation
Correct answer: option 1
We know that,
(Hypotnuese)2 = (Perpendicular)2 + (Base)2
We have,
PT = 10 cm
PA = 5 cm
We also know that,PT2 = AP × PB
PB = PA + AB = 5 + x
100 = 5 × (5 + x)
x = 15
PB = 20
So, ∠PTB = 90°
202 = 102 + BT2
BT = 10√3
Radius of circle = 10√3/2 = 5√3