Answer the following :
ΔPQR 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.
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∠OMQ = m∠OQM = 60°
∴ m∠MOQ = 60°
Similarly, m∠NOR = 60°
Given, QR = 18 cm
∴ r = 9 cm
∴ θ = 60° = `(60 xx pi/180)^"c" = pi^"c"/3`
∴ length of the arc MN = S = rθ
= `9 xx pi/3`
= 3π cm