Two chords AB and CD, of lengths 5 cm and 11 cm respectively, are parallel and are on the same side of the centre O of a circle. If the distance between the chords is 3 cm, then what is the diameter of the circle?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. √146 cm
Let of be 'x' in the given figure.
As we know that the perpendicular from the centre bisects the chord.
⇒ AE = EB = 11/2 cm
⇒ CF = FD = 5/2 cm
In the triangle AOE,
Using Pythagoras theorem
⇒ AO2 = AE2 + OE2
⇒ r2 = (5/2)2 + (x + 3)2
In the triangle COF,
Using Pythagoras theorem
⇒ CO2 = OF2 + CF2
⇒ r2 = (11/2)2 + x2
⇒ (11/2)2 + x2 = (5/2)2 + (x + 3)2
⇒ (11/2)2 = (2.5)2 + 6x + 9
⇒ 6x = 15
⇒ x = 5/2
⇒ r2 = (11/2)2 + x2
⇒ r2 = 121/4 + 25/4
⇒ r2 = 146/4
⇒ r = √(146)/2
⇒ 2r = √146 cm