AB is a diameter of a circle. The length of AB=5cm. If O is the centre of the circle and the length of tangent segment BT=12cm , determime CT ?
Since AB is the diameter and PB is the tangent.
So, AB ⊥ PB (Radius of the circle is perpendicular to the tangent through point of contacy)
⇒ ABC is a right triangle right angled at B
⇒ AT2 = AB2 + BT2 = (5 cm)2 + (12 cm)2 = 25 cm2 + 144 cm2 = 169 cm2 (Pythagoras theorem)
⇒ AT = 13 cm
Now, we know that
If PAB is a secant to a circle intersecting the circle to A and B and PT is a tangent, then PA × PB = PT2
Here is the link for the same.
So,
BT2 = CT × AT
⇒ 144 cm2 = CT × 13 cm
⇒ CT = 144/13 cm