Tangent Triangle with Missing Angle - Rule (Level 1)

This math topic involves solving problems related to the geometry of circles, particularly focusing on tangent triangles and the properties of angles formed when lines tangent to circles intersect such triangles. Students are required to determine relationships between angles, possibly using concepts like supplementary and complementary angles, and equal angles subtended by the same arc. This enhances their understanding of geometric properties and angle calculations in the context of circles and tangents at an intermediate level.

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

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Geometry of Circles - Tangent Triangle with Missing Angle - Rule Worksheet

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Math worksheet on 'Geometry of Circles - Tangent Triangle with Missing Angle - Rule (Level 1)'. Part of a broader unit on 'Geometry - Intermediate - Practice' Learn online: app.mobius.academy/math/units/geometry_intermediate_practice/
1
An svg image showing a math problem
What is known about angle BDC and BCD given that YC forms a tangent?
a
BDC is half BCD
b
Nothing, BDC and BCD are not subtended by the same arc
c
BDC and BCD add to 360º
d
BDC and BCD add to 90º
e
BDC and BCD add to 180º
f
BDC is the same as BCD
2
An svg image showing a math problem
What is known about angle DMC and DCM given that PC forms a tangent?
a
DMC and DCM add to 180º
b
DMC and DCM add to 90º
c
DMC is half DCM
d
DMC and DCM add to 360º
e
DMC is the same as DCM
f
DMC is twice DCM
3
An svg image showing a math problem
What is known about angle ZBR and ZRB given that CR forms a tangent?
a
ZBR and ZRB add to 90º
b
ZBR is half ZRB
c
ZBR and ZRB add to 360º
d
Nothing, ZBR and ZRB are not subtended by the same arc
e
ZBR is the same as ZRB
f
ZBR and ZRB add to 180º
4
An svg image showing a math problem
What is known about angle NXM and NMX given that RM forms a tangent?
a
NXM is half NMX
b
NXM and NMX add to 360º
c
NXM is the same as NMX
d
Nothing, NXM and NMX are not subtended by the same arc
e
NXM and NMX add to 180º
f
NXM and NMX add to 90º
5
An svg image showing a math problem
What is known about angle YDZ and YZD given that XZ forms a tangent?
a
YDZ is the same as YZD
b
YDZ and YZD add to 90º
c
YDZ and YZD add to 180º
d
YDZ is half YZD
e
Nothing, YDZ and YZD are not subtended by the same arc
f
YDZ is twice YZD
6
An svg image showing a math problem
What is known about angle MPC and MCP given that XC forms a tangent?
a
MPC and MCP add to 90º
b
MPC is the same as MCP
c
MPC is twice MCP
d
MPC is half MCP
e
MPC and MCP add to 360º
f
MPC and MCP add to 180º
7
An svg image showing a math problem
What is known about angle XCY and XYC given that PY forms a tangent?
a
XCY is the same as XYC
b
XCY and XYC add to 360º
c
XCY and XYC add to 90º
d
XCY and XYC add to 180º
e
XCY is half XYC
f
XCY is twice XYC