Two parallel chords in a circle are 10 cm and 24 cm long.if the radius of the circle is 13 cm ,find the distance between the chords
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Answer:
Two parallel chords in a circle are 10 cm and 24 cm long . If the radius of the circle is 13 cm ,the distance between the chords is 17 cm.
Step-by-step explanation:
Let the perpendiculars from center to those lines be a and b.
Using Pythagoras theorem,
→ radius² = (1/2 of 10 )² + a²
→ 13² = 5² + a²
→ 169 - 25 = a²
→ 144 = a²
→ 12 = a
Similarly, for b,
→ 13² = (1/2 of 24 )² + b²
→ 13² = 12² + b²
→ 169 - 144 = b²
→ 25 = b²
→ 5 = b
Hence distance between them is a + b = 12 + 5 = 17 cm
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