Answer:
12.5 cm
Explanation:
You want the radius of the circumcircle for an isosceles triangle with base 24 cm and sides 15 cm.
Similar triangles
In the attached, triangle ABC is the given isosceles triangle. CD is its altitude. OE is the perpendicular bisector of BC. Triangles BCD and OBE are similar.
The side ratio BD/BC = 12/15 = 4/5 tells you that ∆BCD is a 3-4-5 right triangle. This, in turn, tells you BE/BO = 3/5.
radius BO = 5·BE/3 = 5·7.5/3
radius BO = 12.5 . . . . cm
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Additional comment
We recognize the right triangles as having side lengths that are multiples of the {3, 4, 5} Pythagorean triple. You could use the Pythagorean theorem relation to find the missing side length if you're unfamiliar with that triple:
BC² = CD² +BD²
CD² = BC² -BD² = 225 -144 = 81
CD = √81 = 9
You can also use trig relations:
angle CBD = arccos(12/15) ≈ 36.869898°
OB = 7.5/sin(angle CBD) = 12.5