Question
Download Solution PDFWhat 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Radius of the circle, r = 7 cm.
Diameter AB and non-diameter chord PQ intersect perpendicularly at point C.
The ratio of AC to BC is 4:3.
Formula Used:
Also, using the property of intersecting chords:
AC × BC = PC × CQ
Calculation:
Radius = 7 cm
Diameter = AB = 2 × Radius
AB = 2 × 7 = 14 cm
AB = AC + BC = 14 cm
AC : BC = 4 : 3
AC = (4/7) × 14 = 8 cm
BC = (3/7) × 14 = 6 cm
Here, PC = CQ (AC is perpendicular to PQ)
So, Using the theorem we get
AC × BC = PC × CQ
8 × 6 = PC × PC
PC2 = 48
PC = 4√3 cm
PQ = PC + CQ = 4√3 + 4√3 = 8√3 cm
∴ The correct answer is Option (4).
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