If radii of two concentric circles are 3cm and 5cm , then find the length of the chord of one circle which is tangent to the other circle.
Answers
If you see the figure attached, you will see the diagram for this question.
Radius of smaller circle, AC = 3 cm ...(i)
Radius of bigger circle, AB = 5 cm ...(ii)
According to the figure, ΔABC is right angled (∵ Radius of a circle meets the tangent of the same circle at right angles.)
We know,
AB² = AC² + BC² (Pythagoras Theorem)
From (i) and (ii),
5² = 3² + BC²
⇒ 25 = 9 + BC²
⇒ 25 - 9 = BC²
⇒ 16 = BC²
⇒√16 = BC
⇒ 4 = BC ...(iii)
Now, In Class 9 we got that the perpendicular to a chord of a circle from the centre bisects the chord.
Here AC ⊥ BD
∴ BC = CD = 2BD ...(iv)
Now,
BC + CD = BD
Using (iv)
BC + BC = BD
⇒ 2BC = BD
From (iii),
2 × 4 = BD
⇒ 8 = BD (Answer)
Answer:
answer = 8 cm
Step-by-step explanation:
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