The diagonal of an isosceles trapezoid is perpendicular to the side. Find the diagonal of the trapezoid

| July 21, 2021 | education

The diagonal of an isosceles trapezoid is perpendicular to the side. Find the diagonal of the trapezoid if the radius of the circumscribed circle is 13 cm and the side side is 10 cm.

1. The tops of the trapezoid – A, B, C, D. AB = 10 cm.

2. We calculate the length of the larger base of the trapezoid AD, taking into account that the radius of the circumscribed circle (R), according to the properties of the trapezoid, in which the diagonal is perpendicular to the lateral side, is equal to 1/2 the length of the base:

AD = R x 2 = 13 x 2 = 26 cm.

3. Calculate the length of the diagonal BD, which in the right-angled triangle ABD is

leg, using the Pythagorean theorem:

BD = √AD² – AD² = √26² – 10² = √676 – 100 = √576 = 24 cm.

Answer: diagonal BD = 24 cm.



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