YoanP574980 YoanP574980

03-11-2022
Mathematics

contestada

QV is tangent to circle O at point Q, and
QB is a secant line. If mQFB = 252°,
find m/BQV.
B
V
F

QV is tangent to circle O at point Q andQB is a secant line If mQFB 252find mBQVBVF class=

Respuesta :

NivanX324182 NivanX324182

03-11-2022

We have to find m∠BQV.

As QV is a tangent line, we can relate ∠BQV with the minor arc QB as:

[tex]\begin{gathered} m\angle BQV=\frac{1}{2}m\overarc{BQ}=\frac{1}{2}(360\degree-m\overarc{BFQ})=\frac{1}{2}(360\degree-252\degree) \\ m\angle BQV=\frac{1}{2}(108\degree) \\ m\angle BQV=54\degree \end{gathered}[/tex]

Answer: m∠BQV = 54°

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