Question

This is circle theorems I am not rly good at this

Answer 1

m∠BCD = 24°

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 =
`(1)/(2)[m(\text{arc BFD})-m(\text{arc BD})]`

=
`(1)/(2)[204 - 156]`

= 24°