What is AQ^{2}+CP^{2} equal to?
Consider the following for the next three (03) items that follow: ABC is a triangle with AB=1.6\text{ cm}, BC=6.3\text{ cm} and CA=6.5\text{ cm}. Let P and Q be the mid-points of AB and BC respectively.
- A. AC^{2}
- B. 1.2AC^{2}
- C. 1.25AC^{2} ✓
- D. 1.5AC^{2}
Correct Answer: C. 1.25AC^{2}
Explanation
In a right triangle right-angled at B, AQ and CP are the medians to the legs. A standard theorem states that 4(AQ^2 + CP^2) = 5AC^2. Thus, AQ^2 + CP^2 = \frac{5}{4}AC^2 = 1.25AC^2.
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