Question

DG and EG are tangent to circle C and circle F. The points of tangency are A, B, D, and E. if M

Answer 1

The correct option is b.

`$\angle A C B` is
`140^(\circ)$`.

To solve for angle ∠ACB, we need to apply a few theorems related to circles and tangents:

1. The Alternate Segment Theorem: This states that the angle between the tangent and the chord through the point of contact is equal to the angle in the alternate segment made by the chord.

2. Angles Subtended on the Same Chord: Angles subtended on the same chord and in the same segment are equal.

3. Tangent-Radius Perpendicularity Theorem: The tangent to a circle is perpendicular to the radius drawn to the point of tangency.

With these theorems in mind, let's go step by step:

• Since
  `\( ED \)` is a tangent to circle C at point B,
  `\( \angle EBC \)` is equal to
  `\( \angle ACB \)` (Alternate Segment Theorem).
• 
  `\( \angle EBC \)` and
  `\( \angle EFD \)` are on the same chord
  `\( ED \)` and therefore,
  `\( \angle EFD = \angle EBC \)` (Angles Subtended on the Same Chord).
• It is given that
  `\( \angle EFD = 140^\circ \)`.

Therefore,
`\( \angle ACB = 140^\circ \)`.

Answer 2

From the question and the given diagram, we were told that:

DG and EG are tangent to circle C and circle F.

The point of tangency are A, B, D, and E.

If M

We are to find m

In solving this, we will have to need or consider the similarity theorem.

Its says that if corresponding angles are congruent, then their angles are similar.

It in essence states that, C