Question 48

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waecmaths question: 

In the diagram $\overline{MN}$is a chord of a circle KMN centre O and radius 10cm. If $\angle MON={{140}^{\circ }}$, find, correct to the nearest cm, the length of the chord MN

Option A: 

19cm

Option B: 

18cm

Option C: 

17cm

Option D: 

12cm

waecmaths solution: 

\[\begin{align}  & ON=OM=10cm\text{    }\!\!\{\!\!\text{ radius of circle }\!\!\}\!\!\text{ } \\ & \text{using cosine rule} \\ & {{\left| MN \right|}^{2}}={{\left| OM \right|}^{2}}+{{\left| ON \right|}^{2}}-2\left| OM \right|\left| ON \right|\cos {{140}^{\circ }} \\ & {{\left| MN \right|}^{2}}={{10}^{2}}+{{10}^{2}}-2(10)(10)\cos {{140}^{\circ }} \\ & {{\left| MN \right|}^{2}}=200-200(-0.7660)=200+153.2 \\ & {{\left| MN \right|}^{2}}=353.2 \\ & \left| MN \right|=\sqrt{353.2}cm=18.79 \\ & \left| MN \right|\approx 19cm\text{ to the nearest cm} \\\end{align}\]

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