Thread: geometry again .

In the diagram , AN and BM are perpendicular to the tangent at R . O is the centre of the circle with diameter AB . Prove that

(1) triangle ANR and RMB are similar

I managed to prove this part

(2) NR=MR

stuck with this .

produce a line AM that intersects with OR at C.
you will see that triangles ACO and AMB are similar.
triangles ANM and CRM are also similar.
Since AO:OB = 1:1
Hence AC:CM = 1:1
and therefore NR:RM = 1:1
which means NR = MR