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XG segment is an angle bisector of ∠YXZ ⇒ C

Step-by-step explanation:

Let us revise the steps of constructing a bisector of an angle

Place compass pin on the vertex of the angle (point X). Open the compass to a suitable length that and draw an arc to intersect the two sides of the angle at two points (points E and F)Place the compass pin on one of these new points on the sides of the angle(point E).  Stretch the compass to a sufficient length and draw an arc in the interior of the angelWithout changing the span on the compass, place the pin of the compass on the other intersection point on the side of the angle (point F) and make a similar arc. The two small arcs in the interior of the angle are intersecting. in a point (point P)Join the vertex of the angle (point X) to this intersection of the two small arcs (point P) XP is the bisector of angle X

By comparing these steps with The steps in the figure, you will find that they are the same steps

∵ XP ray intersect YZ segment at G

∴ G belong to XP ray

∵ XP ray is the bisector of ∠YXZ

∴ XG segment is the bisector of ∠YXZ

Then the statement must be true is:

XG segment is an angle bisector of ∠YXZ

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12