Question
∆PQR is an equilateral triangle with side 18 cm. A circle is drawn on segment QR as diameter. Find the length of the arc of this circle within the triangle.
✓
Answer
Let ‘O’ be the centre of the circle drawn on QR as a diameter.
Let the circle intersect seg PQ and seg PR at points M and N respectively.
Since l(OQ) = l(OM),
m∠OM Q = m∠OQM = 60°
m∠MOQ = 60°
Similarly, m∠NOR = 60°
Given, QR =18 cm.
r = 9 cm
$\theta=60^{\circ}=\left(60 \times \frac{\pi}{180}\right)^c$
$=\left(\frac{\pi}{3}\right)^c$
$\therefore I(\operatorname{arc} M N)=S=r \theta=9 \times \frac{\pi}{3}=3 \pi \mathrm{cm} .$
Let the circle intersect seg PQ and seg PR at points M and N respectively.
Since l(OQ) = l(OM),
m∠OM Q = m∠OQM = 60°
m∠MOQ = 60°
Similarly, m∠NOR = 60°
Given, QR =18 cm.
r = 9 cm
$\theta=60^{\circ}=\left(60 \times \frac{\pi}{180}\right)^c$
$=\left(\frac{\pi}{3}\right)^c$
$\therefore I(\operatorname{arc} M N)=S=r \theta=9 \times \frac{\pi}{3}=3 \pi \mathrm{cm} .$
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