Problem 1095: Externally Tangent Circles, Common Tangent, Radius, Geometric Mean, Metric Relations. Level: High School, SAT Prep, College Geometry

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The figure shows the circles O₁ (radius r₁) and O₂ (radius r₂) tangent at T and tangent to PA₁ and PB₁ at A₁, A₂, B₁, and B₂, respectively. If PA₁ = d₁ and PA₂ = d₂, prove that (1) Formula 1 to prove ; (2) Formula 2 to prove .

$Geometry Problem 1095 Externally Tangent Circles, Common Tangent, Radius, Metric Relations$