Question 28

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Jambmaths question: 

$\begin{align}  & \text{Find the length of a chord which subtends an angle of 9}{{\text{0}}^{\text{o}}}\text{ at the centre of a } \\ & \text{circle whose radius is 8cm} \\ & \text{(A)  }4cm\text{  (B) }8cm\text{  }(C)\text{  }8\sqrt{2}cm\text{  (D) }8\sqrt{3}\text{ cm} \\\end{align}$

Jamb Maths Solution: 

$\begin{align}  & \text{Line OD is perpendicular bisector of line }AB \\ & \text{Also it divide }A\overset{\wedge }{\mathop{O}}\,B\text{ into 4}{{\text{5}}^{\circ }}\text{ each} \\ & \text{Consider the right angle triangle }AOD \\ & \sin {{45}^{\circ }}=\frac{AD}{8cm} \\ & AD=8\sin {{45}^{\circ }}cm=8\times \frac{1}{\sqrt{2}}cm=\frac{8\sqrt{2}}{\sqrt{2}\times \sqrt{2}}cm \\ & AD=\frac{8\sqrt{2}}{2}=4\sqrt{2}cm \\ & AB=2AD\text{  (}OD\text{ is }\bot \text{ar bisector of }AB) \\ & AB=4\sqrt{2}\times 2cm=8\sqrt{2}cm \\\end{align}$

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