Question:
The chord of a circle of radius 10 cm subtends a right angle at its centre. The length of the chord (in cm) is
(a) $\frac{5}{\sqrt{2}} \mathrm{~cm}$
(b) $5 \sqrt{2} \mathrm{~cm}$
(c) $10 \sqrt{2} \mathrm{~cm}$
(d) $10 \sqrt{3} \mathrm{~cm}$
Solution:
In right triangle AOB
By using Pythagoras theorem, we have
AB2 = BO2 + OA2
= 102 + 102
= 100 + 100
= 200
∴OR2 = 200
$\Rightarrow \mathrm{OR}=10 \sqrt{2} \mathrm{~cm}$
Hence, the correct answer is option (c).
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