I need help with a geometry problem!

Short Answer: D
Start with the givens.
MP is the base of an isosceles Δ   Given
HM = HP                                        The Triangle is isosceles. Two sides are =
NM = OP                                        Given
NP ⊥ OM                                        Where they meet forms a right angle.

Other things that can be proven.
<NHM = <OHP      Lines that are ⊥ form right angles where the lines meet.

Conclusion
We have 2 right angle triangles. They have equal hypotenuses. They have 1 other side that is congruent to a corresponding side of the other triangle

The triangles are congruent by HL

 D <<<< Answer