In  △ABC, P  and  Q  are mid points of sides  AB  and  BC  respectively, right angled at  B,  thenSelect an answerA AQ2 + CP2  =  AC2 B AQ2 + CP2  =  4/5AC2 C AQ2 + CP2  =  3/4AC2 D AQ2 + CP2  =  5/4AC2

Given that P and Q are midpoints of sides AB and BC respectively, we can say that AP = PB = 1/2AB and BQ = QC = 1/2BC.

Since triangle ABC is right angled at B, by Pythagoras theorem, we have:

AC² = AB² + BC²

Substituting the values of AB and BC, we get:

AC² = (2AP)² + (2BQ)²

AC² = 4AP² + 4BQ²

Now, we need to find the value of AQ² + CP².

We know that AQ² = AP² + PQ² and CP² = PQ² + QC².

Substituting the values of AP, PQ and QC, we get:

AQ² = (1/2AB)² + (AB/2 + BC/2)² and CP² = (AB/2 + BC/2)² + (1/2BC)²

Solving these equations, we get:

AQ² = 1/4AB² + 1/4(AB² + 2AB.BC + BC²) and CP² = 1/4(AB² + 2AB.BC + BC²) + 1/4BC²

Adding AQ² and CP², we get:

AQ² + CP² = 1/4AB² + 1/4BC² + 1/2(AB² + 2AB.BC + BC²)

Simplifying, we get:

AQ² + CP² = 3/4AB² + 3/4BC² + 1/2AB.BC

Comparing this with the equation AC² = 4AP² + 4BQ², we can see that AQ² + CP² is not equal to AC², 4/5AC², 3/4AC² or 5/4AC².

Therefore, none of the options A, B, C, D are correct.