Circle question?

Draw a circle and two congruent chords FH and JI that intersect at point E (not the center O). Draw radii OF, OH, OI, and OJ. Prove that angle OFH, angle FHO, angle OJI, and angle JIO are congruent.

1 Answer

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  • 4 years ago
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    According to the conditions given, we know

    (1) OI=OF=OJ=OH (radii of same circle O)

    (2) JI=FH (given)

    (3) Tri.JOI is congruent to Tri.FOH (s.s.s)

    (4) <JIO=<HFO, <OJI=<OHF

    (the corresponding angles equal)

    (5) <OIJ=<OJI, <OHF=<HFO

    (the base angles of an isosceles triangles equal)

    (6) <OJI=<OIJ=<OFH=<OHF (substitutions)

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