O is the center of a circle with a diameter 20 cm. T is a point outside the circle and TA is a tangent to a circle. If OT is = 26cm, what is the length (in cm) of the tangent TA?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 24
Diameter of the circle = 20 cm
OT = 26 cm
Radius = Diameter/2
The radius of a circle is always perpendicular to the tangent on the circle.
In a right-angled triangle -
Base = √(Hypotenuse2 - Perpendicular2)
OT = 26 cm
Radius (OA) = 20/2 = 10 cm
OA is perpendicular to TA.
∠OAT = 900
In ΔOAT -
TA = √(262 - 102) = √(676 - 100) = √576 = 24 cm