 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-1/4/a/solution

The two equal legs meet at the right angle, so the Pythagorean theorem gives

A B^{2} + A C^{2} = B C^{2} = 4

, with

A B = A C

. Thus

A C = 2

. The midpoint condition then yields

A D = \frac{A C}{2} = \frac{1}{2} units .

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