If (ma + nb) : b : : (mc + nd) : d, prove that a, b, c, d are in proportion.
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If (4a + 5b)(4c - 5d) = (4a - 5b)(4c + 5d), prove that a, b, c, d are in proportion.
If (pa + qb) : (pc + qd) : : (pa - qb) : (pc - qd), prove that a : b : : c : d.
If (11a2 + 13b2)(11c2 - 13d2) = (11a2 - 13b2)(11c2 + 13d2), prove that a : b : : c : d.