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tangents to circle from point

Source: LIMIT 2019 CAS2 P4

April 28, 2021
geometry

Problem Statement

From a point PP outside of a circle with centre OO, tangent segments PA‾\overline{PA} and PB‾\overline{PB} are drawn. If 1∣OA‾∣2+1∣PA‾∣2=116\frac1{\left|\overline{OA}\right|^2}+\frac1{\left|\overline{PA}\right|^2}=\frac1{16}, then ∣AB‾∣=\left|\overline{AB}\right|=? <spanclass=′latex−bold′>(A)</span> 4<span class='latex-bold'>(A)</span>~4 <spanclass=′latex−bold′>(B)</span> 6<span class='latex-bold'>(B)</span>~6 <spanclass=′latex−bold′>(C)</span> 8<span class='latex-bold'>(C)</span>~8 <spanclass=′latex−bold′>(D)</span> 10<span class='latex-bold'>(D)</span>~10
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