Answer:
m∠BCD = 24°
Step-by-step explanation:
By the theorem,
"Angle subtended by an arc at the center of the circle is twice in measure of the angle subtended at the circumference."
m(∠BOD) = 2(m∠BFD)
= 2(78°)
= 156°
Therefore, m(arc BD) = m∠BOD = 156°
Since, m(arc BD) + m(arc BFD) = 360°
156° + m(arc BFD) = 360°
m(arc BFD) = 360 - 156
= 204°
Since, "angle formed outside the circle by the intersection of two tangents measure half of the difference of the intercepted arcs".
m∠BCD = [tex]\frac{1}{2}[m(\text{arc BFD})-m(\text{arc BD})][/tex]
= [tex]\frac{1}{2}[204 - 156][/tex]
= 24°
