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Isosceles Triangle ABC has each leg measuring 13 cm and is inscribed in circle O as shown below. If the altitude to the base of the triangle is 5cm, calculate the radius of the circle.

Isosceles Triangle ABC has each leg measuring 13 cm and is inscribed in circle O as shown below If the altitude to the base of the triangle is 5cm calculate the class=

Respuesta :

Radius = 5 + x

Also we have two similar triangles whose corresponding sides are proportional, hence:

Proportion may be 13 : 5 = (5 + x) : 13/2

5 · (5 + x) = 13²/2

5 x + 25 = 169/2

5 x = 169/2 - 25

x = 11.9

Then, R (radius) = 5 + x = 11.9 + 5 = 16.9 units

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