Question

Plz answer fast and right​

Answer 1

Circles with centres X and Y touch internally point Z.

Join YZ.

(Refer image)

By theorem of touching circles, points Y, X, Z are collinear.

Now, segXA≅segXZ (Radii of circle with centre X)

∴∠XAZ=∠XZA (Isosceles triangle theorem) (1)

Similarly, segYB≅segYZ (Radii of circle with centre Y) ∴∠BZY=∠ZBY (Isosceles triangle theorem) (2) From (1) and (2), we have ∠XAZ=∠ZBY

If a pair of corresponding angles formed by a transversal on two lines is congruent, then the two lines are parallel.

∴segAX∣∣segBY (Corresponding angle test)