std 9 geometry lesson 6 circles activity 1 properties of chords table
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QUESTION:
Distance of chord AB from the centre of a circle is 8 cm. Length of the chord AB is 12 cm. Find the diameter of the circle.
ANSWER:
Let the centre of the circle be O.
AB = 12 cm
OC = 12 cm
OC ⊥ AB
We know perpendicular drawn from the centre of the circle to the chord, bisects the chord.
So, AC = 6 cm
In ⃤ OCA,
OC²+AC²=AO²
⇒8²+6²=AO²
⇒AO²=100
⇒AO=10
Thus, AO = 10 cm
Diameter = 2 × 10 cm = 20 cm.
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