Circle: Angles

Cyclic Quadrilateral

 

Cyclic Quadrilateral

The opposite angles of a cyclic quadrilateral are supplementary

 

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\begin{equation*} \begin{split} \color {blue} \text{m}\angle \text{a} +  \text{m}\angle \text{c} & \color {blue} \:= 180^{\circ}\\\\ \color {red} \text{m}\angle \text{b} +  \text{m}\angle \text{d} & \color {red}\:= 180^{\circ}\\\\ \end{split} \end{equation*}

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If T is the point of intersection of the two diagonals, then \(\color{blue} \text{AT}\times \text{TC} = \text{BT}\times \text{TD}\)

 

Exercise

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