What is the length (in cm) of chord PQ in a circle with a radius of 7 cm, where a diameter AB and non-diameter chord PQ intersect perpendicularly at point C, and the ratio of AC to BC is 4 : 3?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 8√3.
As seen in the figure
AC : CB = 4 : 3
Let the common ratio be x
Hence AC : CB = 4x : 3x
Given that the length of the diameter = 7 + 7 = 14
Hence, 4x + 3x = 14
⇒ x = 2
Hence, AC = 8 and CB = 6
Now in △POC, PO = 7 and OC = 8 - 7 = 1
Using Pythagoras theorem we get PC = √48
Hence the length of PQ = 2√48 = 8√3 cm.