Question

A)
The radius of a circle circumscribed about a triangle has radii that reach from the vertices of thetriangle to the
(1 point)
circumcenter.
incenter.
centroid.
orthocenter.
A)
Arlo wants to prove that opposite angles of quadrilaterals inscribed in circles are supplementary.They consider quadrilateral
inscribed in circle
. They want to prove that
and
are supplementary. Which of the following should they use as their proof?
(1 point)
GTRY M ∠R
∠G
Together, the intercepted arcs of
and
create circle
, which measures 360°. Inscribed angles areequal to the measures of their intercepted arcs, so the sum of the measures of
and
is 360°.Therefore,
and
are supplementary.
∠
R
∠
G
M
∠
R
∠
G
∠
R
∠
G
Together, the intercepted arcs of
and
create circle
, which measures 360°. Inscribed angles arehalf the measures of their intercepted arcs, so the sum of the measures of
and
is 180°.Therefore,
and
are supplementary.
∠
R
∠
G
M
∠
R
∠
G
∠
R
∠
G
Together, the intercepted arcs of
and
create circle
, which measures 180°. Inscribed angles arehalf the measures of their intercepted arcs, so the sum of the measures of
and
is 90°. Therefore,
and
are supplementary.
∠
R
∠
G
M
∠
R
∠
G
∠
R
∠
G
Together, the intercepted arcs of
and
create circle
, which measures 180°. Inscribed angles areequal to the measures of their intercepted arcs, so the sum of the measures of
and
is 180°.Therefore,
and
are supplementary.

Answer 1

1) circumcenter.

2) The correct proof is the one that says: together the intercepted arcs add to 360°, and inscribed angles measure half their intercepted arcs, so the two angles sum to 1/2·360° = 180° and are supplementary.