Answer: The answer is (D). the image is attached.
Step-by-step explanation: We are given four figures from which we are to select the one with AB = AC.
In figure (A), AB and AC are two chords of the circle with common point A. Since the lengths of two chords of a circle may not be equal, so AB may not be equal to AC. This option is not correct.
In figure (B), AB is a tangent at point B and AC is the extension of a chord which meets the tangent AB at point A. Since the lengths of AB and AC may not be equal, so this option is also incorrect.
In figure (C), AB and AC are extensions of two chords which meets at point A outside the circle, so they may not be congruent. So, this option will also not work.
In figure (D), AB and AC are two tangents from a common point A to the circle at B and C respectively.
We have the Two-Tangent Theorem which states that if two tangent segments are drawn to one circle from the same external point, then they are congruent.
So, we have AB ≅ AC.
Thus, (D) is the correct option.
