Two chords of length 20 cm and 24 cm are drawn perpendicular to each other in a circle of radius is ...........

Quantitative Aptitude (CGL) Coordinate Geometry

Two chords of length 20 cm and 24 cm are drawn perpendicular to each other in a circle of radius is 15 cm. What is the distance between the Points of intersection of these chords (in cm) from the center of the circle?

√114

√182

√206

√218

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Explanation:

Given: Radius 15 cm, AB = 24 cm
And CD = 20 cm
To find FG = ?
So here we begin....
In Δ BOG,
(OG)² = (OB)² - (BG)²
(OG)² = (15)² - (12)²
(OG)² = 225 - 144 = 81.......(1)
Similarly, in Δ COF,
(OF)² = (OC)² - (CF)²
(OF)² = (15)² - (10)²
(OF)² = 225 - 100 = 125....(2)
Again in Δ GOF,
(FG)² = (OF)² + (OG)²
(FG)² = 125 + 81 = 206
(FG)² = √206