Question
Download Solution PDFIf the area of a circle is 616 cm2 and a chord XY = 10 cm, then find the perpendicular distance from the center of the circle to the chord XY.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Area of circle = 616 cm2
Chord = XY = 10 cm
Concept used:
The perpendicular line from the centre divides the chord into two equal parts.
Formula used:
Pythagorean theorem:
H2 = P2 + B2
Where, H = hypotenuse ; P = perpendicular ; B = base
Area of circle = π × R2
Calculation:
Area of circle = 616 cm2
⇒ π × R2 = 616
⇒ R2 = (616 × 7)/22
⇒ R = √(28 × 7) = 14 cm
OX = 14 cm
XY = 10 cm
OC ⊥ XY
XC = 10/2 = 5 cm
By Pythagorean theorem
⇒ H2 = P2 + B2
⇒ (OX)2 = (OC)2 + (XC)2
⇒ (14)2 = (OC)2 + (5)2
⇒ (OC)2 = 196 - 25 = 171
⇒ OC = √171
∴ The correct answer is √171.
Last updated on Jun 13, 2025
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