The diameter PQ of a circle with center O is perpendicular to the chord RS. PQ Intersects RS at T. If RS = 16 cm and QT = 4 cm, what is the length (in cm) of the diameter of the circle?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 20.
Let RO = r [RO os the radius of the circle] then,
⇒ OT = OQ - QT
⇒ OT = r - 4 and
⇒ RT = RS/2 = 16/2 = 8 cm
In △ROT
⇒ OR2 = RT2 + OT2
⇒ r2 = 82 + (r - 4)2
⇒ r2 = 64 + r2 + 16 - 8r
⇒ 80 = 8r
⇒ r = 10
Thus, the diameter of the circle = 2 × radius = 2 × 10 = 20 cm