10 (a) E D NOT TO SCALE C F A B ABCDEF is a regular hexagon. DF, DA and DB are diagonals. Complete the following statements using three different triangles. Triangle DEF is congruent to triangle .................. Triangle .................. is congruent to triangle .................. [2] (b) Q NOT TO SCALE O T P P and Q are points on the circle with centre O. TP and TQ are tangents to the circle from the point T. Complete the following statements and reasons. In triangles OPT and OQT OP = .................. because each is a radius of the circle OT is a common side Angle OPT = angle .................. = 90° because .............................................................................. Triangles OPT and OQT are congruent using the criterion .................. This proves that the tangents TP and TQ are .................................................. [5] © UCLES 2023 0580/42/O/N/23 [Turn over 16 3 2 !