Question
Download Solution PDFA circle of diameter 26 cm has two equal chords of length 10 cm each, separated by a distance h cm. What is the value of h?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Diameter of the circle = 26 cm
Radius of the circle (r) = 26/2 = 13 cm
Length of the chords = 10 cm each
Distance between the two chords = h cm
Formula used:
For a chord of length 2a, the perpendicular distance from the center of the circle is given by:
d = √(r2 - a2)
Where r = radius, a = half of the chord length
Calculation:
Half of the chord length (a) = 10/2 = 5 cm
Using the formula for the perpendicular distance:
d = √(132 - 52)
d = √(169 - 25) = √144
⇒ d = 12 cm
The distance between the two chords = 2d = 2 × 12 = 24 cm
∴ The value of h is 24 cm.
Last updated on May 28, 2025
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