Geometry of Circles - Rule for Inscribed Angle from Intersected Arc (Level 1)

This math topic focuses on the geometric properties of circles, specifically the relationship between inscribed angles and the arcs they intersect. Students are required to apply and interpret the rule that an inscribed angle is half the measure of its intercepted arc, or variations of this rule. They are presented with diagrams of circles containing various points and arcs and are asked to compare the angular measurements of inscribed angles to the lengths of the corresponding arcs. Each problem presents multiple-choice answers, challenging students to distinguish correct relationships in the context of circle geometry.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

Geometry of Circles - Rule for Inscribed Angle from Intersected Arc Worksheet

Math worksheet on 'Geometry of Circles - Rule for Inscribed Angle from Intersected Arc (Level 1)'. Part of a broader unit on 'Geometry - Intermediate - Intro' Learn online: app.mobius.academy/math/units/geometry_intermediate_intro/

1

What is known about angle MRC compared to the length (in degrees) of intersected arc MC?

a

MC and MRC add to 90º

b

Nothing, MC and MRC are not subtended by the same arc

c

MC is the same as MRC

d

MRC is half MC

e

MC and MRC add to 360º

f

MC is twice MRC

2

What is known about angle DYN compared to the length (in degrees) of intersected arc DN?

a

DN and DYN add to 360º

b

DN and DYN add to 180º

c

Nothing, DN and DYN are not subtended by the same arc

d

DN is the same as DYN

e

DYN is half DN

f

DN is half DYN

3

What is known about angle NCY compared to the length (in degrees) of intersected arc NY?

a

NCY is half NY

b

NY is half NCY

c

NY is the same as NCY

d

NY and NCY add to 90º

e

NY is twice NCY

f

Nothing, NY and NCY are not subtended by the same arc

4

What is known about angle DRM compared to the length (in degrees) of intersected arc DM?

a

Nothing, DM and DRM are not subtended by the same arc

b

DM and DRM add to 360º

c

DM is half DRM

d

DRM is half DM

e

DM and DRM add to 90º

f

DM is twice DRM

5

What is known about angle BDY compared to the length (in degrees) of intersected arc BY?

a

BDY is half BY

b

BY is the same as BDY

c

BY and BDY add to 90º

d

BY is twice BDY

e

BY and BDY add to 360º

f

Nothing, BY and BDY are not subtended by the same arc

6

What is known about angle ZPC compared to the length (in degrees) of intersected arc ZC?

a

ZC is twice ZPC

b

ZC and ZPC add to 360º

c

ZC and ZPC add to 180º

d

Nothing, ZC and ZPC are not subtended by the same arc

e

ZPC is half ZC

f

ZC and ZPC add to 90º

7

What is known about angle CPZ compared to the length (in degrees) of intersected arc CZ?

a

CZ and CPZ add to 90º

b

CZ is half CPZ

c

CZ is the same as CPZ

d

CZ and CPZ add to 360º

e

CPZ is half CZ

f

CZ is twice CPZ