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Omni-MATH / Given the condition that there exist exactly 1990 triangles ABC with integral side-lengths satisfying the following conditions: (i) ∠ABC=(1)/(2)∠BAC; (ii) AC=b. Find the minimal va…

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problem

Given the condition that there exist exactly 19901990 triangles ABCABC with integral side-lengths satisfying the following conditions: (i) ∠ABC=12∠BAC;\angle ABC =\frac 12 \angle BAC; (ii) AC=b.AC = b. Find the minimal value of b.b.
Plain-text mathematical notation (without MathML)
Given the condition that there exist exactly 1990 triangles ABC with integral side-lengths satisfying the following conditions:
(i) ∠ABC=(1)/(2)∠BAC;
(ii) AC=b.
Find the minimal value of b.
Original LaTeX notation
Given the condition that there exist exactly $1990$ triangles $ABC$ with integral side-lengths satisfying the following conditions:
(i) $\angle ABC =\frac 12 \angle BAC;$
(ii) $AC = b.$
Find the minimal value of $b.$

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Source and history

task_id
93b10b4b-8115-5037-9295-c024f546fc2a
task_key
test--93b10b4b-8115-5037-9295-c024f546fc2a
task_revision_id
1
config / split
/ test

Official source

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