Two concentric circles of radii 5 cm and 3 cm are drawn. Find the length of the chord of the larger circle which touches the smaller circle.
Answers
Answer:
see attachment
Explanation:
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Qᴜᴇsᴛɪᴏɴ :-
Two concentric circles of radii 5 cm and 3 cm are drawn. Find the length of the chord of the larger circle which touches the smaller circle.
Sᴏʟᴜᴛɪᴏɴ :-
Given : Two circles of radii 3 cm & 5 cm with common centre.
[Refer the attachment for the diagram]
Let AB be a tangent to the inner/small circle and chord to the larger circle.
Let 'P' be the point of contact.
Construction : Join OP and OB.
Now, In ∆OPB ∠OPB = 90°
[radius is perpendicular to the tangent]
- OP = 3cm
- OB = 5cm
Using Pythagoras theorem
➳ 5² = 3² + PB²
➳ PB² = 25 - 9
➳ PB² = 16
➳ PB = √16
➳ PB = 4
⛬ PB = 4 cm
Now, AB = 2 × PB (The perpendicular drawn from the centre of the circle to a chord, bisects it)
➳ AB = 2 × 4 = 8 cm
⛬ The length of the chord of the larger circle which touches the smaller circle is 8 cm.
