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tmua.me Extreme Set C Paper 2 · Q8

Paper 2Geometry

Triangle ABCABC has

AB=10,BC=17,CA=5.AB=\sqrt{10},\qquad BC=\sqrt{17},\qquad CA=\sqrt5.

A point PP lies strictly inside the triangle and satisfies

∠APB=90∘,∠BPC=∠CPA=135∘.\angle APB=90^\circ,\qquad \angle BPC=\angle CPA=135^\circ.

What is the value of PA+PB+PCPA+PB+PC?

A44
B4+24+\sqrt2
C3+23+\sqrt2
D4+224+2\sqrt2
E66
F22\sqrt{22}

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