You can throw you hands up

Geometry Level 3

In the figure above, P T PT , P R PR and B A BA are the tangents to the circle. If ∠ B P A = 7 0 ∘ \angle BPA =70^\circ , what is the value of ∠ A O B \angle AOB ?


The answer is 55.

Raven Herd by Raven Herd , 21, India

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1 solution

Marta Reece
Aug 19, 2017

From P R O T PROT we get ∡ R O T = 36 0 ∘ − 2 × 9 0 ∘ − 7 0 ∘ = 11 0 ∘ \measuredangle ROT=360^\circ-2\times90^\circ-70^\circ=110^\circ

∡ R O B = ∡ B O S \measuredangle ROB=\measuredangle BOS and ∡ S O A = ∡ A O T \measuredangle SOA=\measuredangle AOT

Therefore ∡ B O A = 11 0 ∘ 2 = 5 5 ∘ \measuredangle BOA=\dfrac{110^\circ}2=\boxed{55^\circ}

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