Regents Exam Questions G.G.51: Arcs Determined by Angles 6
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Name: __________________________________
G.G.51: Arcs Determined by Angles: Investigate theorems about the arcs determined by
angles intersecting a circle when the vertex is on the circle
1 Chords
tangent
Determine
and
intersect at E in circle O, as shown in the diagram below. Secant
are drawn to circle O from external point F and chord
is drawn. The
, and the ratio of
.
. Determine
. Determine
2 Given circle O with diameter
; secants
; and chord
1 ANS:
and
,
.
and
intersect at point H;
. Find the ratio of
to
.
Regents Exam Questions G.G.51: Arcs Determined by Angles 6
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Name: __________________________________
52, 40, 80.
.
.
REF: 081238ge
2 ANS:
2:1.
and
respectively.
measures 144°
and
form a semi-circle and measure 126°
and 54°
,
measures 36°.
and
form a semi-circle and measure 126°.
Equal chords intercept equal arcs. Because chord
chord
each measures 72°
inscribed angle is half that of its intercepted arc. So
The measure of an
The angle formed by a
tangent and a secant is equal to half the difference between the intercepted arcs.
The ratio of
REF: 080333b
2ND SIDE OF SHEET
to
is 54:27, or 2:1.
.
Regents Exam Questions G.G.51: Arcs Determined by Angles 6
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Name: __________________________________
1 In the accompanying diagram,
to circle O at B, and
Find:
,
,
,
2 In the accompanying diagram,
.
Find
,
1 ANS:
40, 60, 70, 50, 60
2 ANS:
90, 45, 40, 95, 30
,
,
is inscribed in circle O,
bisects
,
is tangent
,
is a diameter of circle O,
, and
and
are secants,