In the diagram, $$\(A B C\)$$ is a semicircle with diameter $$\(A C\)$$, centre $$\(O\)$$ and radius $$\(6 \mathrm{~cm}\)$$. The length of the $$\(\operatorname{arc} A B\)$$ is $$\(15 \mathrm{~cm}\)$$. The point $$\(X\)$$ lies on $$\(A C\)$$ and $$\(B X\)$$ is perpendicular to $$\(A X\)$$. Find the perimeter of the shaded region $$\(B X C\)$$. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ 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Exam No：9709_s20_qp_11 Year：2020 Question No：8
Answer:
Angle \(A O B=15 \div 6=2.5\) radians
Angle \(B O C=\pi-2.5(\mathbf{F}\) T on angle \(\mathrm{AOB})\)
\[
B C=6(\pi-2.5) \quad(B C=3.850)
\]
\[
\sin (\pi-2.5)=B X \div 6 \quad(B X=3.59)
\]
Either \(O X=6 \cos (\pi-2.5)\) or Pythagoras \((O X=4.807)\)
\[
X C=6-O X \quad(X C=1.193) \rightarrow P=8.63
\]
Angle \(B O C=\pi-2.5(\mathbf{F}\) T on angle \(\mathrm{AOB})\)
\[
B C=6(\pi-2.5) \quad(B C=3.850)
\]
\[
\sin (\pi-2.5)=B X \div 6 \quad(B X=3.59)
\]
Either \(O X=6 \cos (\pi-2.5)\) or Pythagoras \((O X=4.807)\)
\[
X C=6-O X \quad(X C=1.193) \rightarrow P=8.63
\]
Knowledge points:
1.4.2 use the formulae in solving problems concerning the arc length and sector area of a circle (Including calculation of lengths and angles in triangles and areas of triangles.)
Solution:
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