Question

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Answer 1

$A,B,C,D \ puncte \ pe \ cerc$

m(arc ABC) = m(arc AB)+m(arc BC) = 140°+40° = 180° ⇒ AC este diametru

m(∢ABC) = m(∢ADC) = 90°

m(arc BCD) = m(arc BC)+m(arc CD) = 40°+120° = 160°

m(∢DAB) = ½×m(arc BCD) = ½×160° = 80°

m(arc AD) = m(arc ADC)-m(arc CD) = 180°-120° = 60°

m(arc BAD) = m(arc AB)+m(arc AD) = 140°+60° = 200°

m(∢BCD) = ½×m(arc BAD) = ½×200° = 100°

m(∢BCA) = ½×m(arc AB) = ½×140° = 70°