CONTOH SOAL 8 LINGKARAN (SUDUT ANTARA DUA TALI BUSUR)

 $\begin{aligned}36.\quad&\textrm{Perhatikan gambar berikut}\end{aligned}$.

$\begin{aligned}\quad\qquad&\textrm{Jika}\:\: \angle AOC=151^{\displaystyle 0},\: \angle BOD=23^{\displaystyle 0},\:\: \textrm{maka}\:\:\: \angle AEC=\: .... \\ &\text{a}.\quad 87^{\displaystyle 0}\\ &\text{b}.\quad 78^{\displaystyle 0}\\ &\text{c}.\quad 69^{\displaystyle 0}\\ &\text{d}.\quad 64^{\displaystyle 0}\\\\ &\textrm{Jawab}:\quad \textbf{a}\\ &\begin{aligned}&\textrm{Ingat sudut antara dua tali busur, yaitu:}\\ &\angle AEC=\displaystyle \frac{1}{2}\left( \angle AOC+\angle BOD \right)=\displaystyle \frac{1}{2}\left( 151^{\displaystyle 0}+23^{\displaystyle 0} \right)\\ &\:\quad\qquad=\displaystyle \frac{1}{2}\left( 174^{\displaystyle 0} \right)=87^{\displaystyle 0} \end{aligned}\end{aligned}$.

 $\begin{aligned}37.\quad&\textrm{Perhatikan gambar berikut}\end{aligned}$.

$\begin{aligned}\quad\qquad&\textrm{Jika}\:\: \angle BOD=50^{\displaystyle 0},\: \angle AOC=110^{\displaystyle 0},\:\: \textrm{maka}\:\:\: \angle AEC=\: .... \\ &\text{a}.\quad 60^{\displaystyle 0}\\ &\text{b}.\quad 75^{\displaystyle 0}\\ &\text{c}.\quad 80^{\displaystyle 0}\\ &\text{d}.\quad 120^{\displaystyle 0}\\\\ &\textrm{Jawab}:\quad \textbf{c}\\ &\begin{aligned}&\textrm{Ingat sudut antara dua tali busur, yaitu:}\\ &\angle AEC=\displaystyle \frac{1}{2}\left( \angle AOC+\angle BOD \right)=\displaystyle \frac{1}{2}\left( 110^{\displaystyle 0}+50^{\displaystyle 0} \right)\\ &\:\quad\qquad=\displaystyle \frac{1}{2}\left( 160^{\displaystyle 0} \right)=80^{\displaystyle 0} \end{aligned}\end{aligned}$.

$\begin{aligned}38.\quad&\textrm{Perhatikan gambar berikut}\end{aligned}$.

$\begin{aligned}\quad\qquad&\textrm{Jika}\:\: \angle BCD=68^{\displaystyle 0},\: \angle AEC=105^{\displaystyle 0},\:\: \textrm{maka}\:\:\: \angle ADC=\: .... \\ &\text{a}.\quad 87^{\displaystyle 0}\\ &\text{b}.\quad 73^{\displaystyle 0}\\ &\text{c}.\quad 37^{\displaystyle 0}\\ &\text{d}.\quad 240^{\displaystyle 0}\\\\ &\textrm{Jawab}:\quad \textbf{c}\\ &\begin{aligned}&\textrm{Ingat sudut keliling}\\ &\angle CEB=180^{\displaystyle 0}-105^{\displaystyle 0}=75^{\displaystyle 0}\:\: (\textrm{pelurus sudut})\\ &\textrm{Selanjutnya perhatikan bahwa pada}\: \bigtriangleup CEB\\ &\textrm{total sudutnya}=180^{\displaystyle 0}\\&\angle C+\angle E+\angle B=180^{\displaystyle 0}\Leftrightarrow 68^{\displaystyle 0}+75+\angle B^{\displaystyle 0}=180^{\displaystyle 0}\\ &\Leftrightarrow \angle B=\angle EBC=37^{\displaystyle 0}\\ &\textrm{Dan kita juga tahu bahwa}:\angle EBC=\angle ADC=37^{\displaystyle 0}\\ &(\textrm{Sama-sama sudut keliling menghdap busur yang sama}) \end{aligned}\end{aligned}$.

$\begin{aligned}39.\quad&\textrm{Perhatikan gambar berikut}\end{aligned}$.

$\begin{aligned}\quad\qquad&\textrm{Jika}\:\: \angle BCD=41^{\displaystyle 0},\: \angle ABC=83^{\displaystyle 0},\:\: \textrm{maka}\:\:\: \angle AEC=\: .... \\ &\text{a}.\quad 42^{\displaystyle 0}\\ &\text{b}.\quad 41^{\displaystyle 0}\\ &\text{c}.\quad 40^{\displaystyle 0}\\ &\text{d}.\quad 21^{\displaystyle 0}\\\\ &\textrm{Jawab}:\quad \textbf{a}\\ &\begin{aligned}&\textrm{Perhatikan bahwa pada}\:\: \bigtriangleup CEB\\ &\angle BCE+\angle BEC=\angle ABC\\ &\Leftrightarrow 41^{\displaystyle 0}+\angle BEC=83^{\displaystyle 0}\\ &\Leftrightarrow \angle BEC=\angle AEC=83^{\displaystyle 0}-41^{\displaystyle 0}=42^{\displaystyle 0}\end{aligned}\end{aligned}$.

$\begin{aligned}40.\quad&\textrm{Perhatikan gambar berikut}\end{aligned}$.

$\begin{aligned}\quad\qquad&\textrm{Jika}\:\: \angle AFC=105^{\displaystyle 0},\: \angle BCD=28^{\displaystyle 0},\:\: \textrm{maka}\:\:\: \angle AEC=\: .... \\ &\text{a}.\quad 75^{\displaystyle 0}\\ &\text{b}.\quad 47^{\displaystyle 0}\\ &\text{c}.\quad 45^{\displaystyle 0}\\ &\text{d}.\quad 40^{\displaystyle 0}\\\\ &\textrm{Jawab}:\quad \textbf{b}\\ &\begin{aligned}&\textrm{Ingat segiempat tali busur}\:\: \angle AFC+\angle ABC=180^{\displaystyle 0}\\ &\Leftrightarrow 105^{\displaystyle 0}+\angle ABC=180^{\displaystyle 0}\Leftrightarrow \angle ABC=75^{\displaystyle 0}\\ &\textrm{Perhatikan segitiga}\quad \bigtriangleup BEC\\ &\angle AEC+\angle BEC=\angle ABC\\&\Leftrightarrow \angle AEC+28^{\displaystyle 0}=75^{\displaystyle 0}\\ &\Leftrightarrow \angle AEC=75^{\displaystyle 0}-28^{\displaystyle 0}=47^{\displaystyle 0}\end{aligned}\end{aligned}$.