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Triangle Problem

Source: 1992 National High School Mathematics League, Exam One, Problem 4

February 26, 2020

Problem Statement

In △ABC\triangle ABC, b≠1b\neq1. If CA\frac{C}{A} and sin⁡Bsin⁡A\frac{\sin B}{\sin A} are solutions to equation log⁡bx=log⁡b(4x−4)\log_{\sqrt{b}}x=\log_{b}(4x-4), then △ABC\triangle ABC (A)\text{(A)}is an isosceles triangle, but not right-angled triangle (B)\text{(B)}is a right-angled triangle, but not isosceles triangle (C)\text{(C)}is an isosceles right-angled triangle (D)\text{(D)}is neither a right-angled triangle nor an isosceles triangle
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