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.
Practice:
Tangent Triangle with Missing Angle - Rule
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What is known about angle MPC and MCP given that XC forms a tangent?
Geometry of Circles - Tangent Triangle with Missing Angle - Rule Worksheet
| 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/ |
| What is known about angle CPR and CRP given that NR forms a tangent? |
| Nothing, CPR and CRP are not subtended by the same arc |
| CPR is twice CRP |
| CPR is the same as CRP |
| CPR and CRP add to 90º |
| CPR is half CRP |
| CPR and CRP add to 360º |
| What is known about angle CYX and CXY given that BX forms a tangent? |
| CYX is the same as CXY |
| CYX and CXY add to 90º |
| CYX is twice CXY |
| CYX and CXY add to 180º |
| CYX is half CXY |
| CYX and CXY add to 360º |
| What is known about angle BDC and BCD given that YC forms a tangent? |
| BDC is the same as BCD |
| Nothing, BDC and BCD are not subtended by the same arc |
| BDC and BCD add to 90º |
| BDC and BCD add to 180º |
| BDC is half BCD |
| BDC and BCD add to 360º |
| What is known about angle YDZ and YZD given that XZ forms a tangent? |
| Nothing, YDZ and YZD are not subtended by the same arc |
| YDZ and YZD add to 180º |
| YDZ is the same as YZD |
| YDZ is twice YZD |
| YDZ and YZD add to 90º |
| YDZ is half YZD |
| What is known about angle YCM and YMC given that BM forms a tangent? |
| YCM is half YMC |
| YCM is twice YMC |
| YCM and YMC add to 90º |
| YCM is the same as YMC |
| YCM and YMC add to 360º |
| YCM and YMC add to 180º |
| What is known about angle ZBR and ZRB given that CR forms a tangent? |
| ZBR is the same as ZRB |
| ZBR is half ZRB |
| ZBR and ZRB add to 180º |
| Nothing, ZBR and ZRB are not subtended by the same arc |
| ZBR and ZRB add to 90º |
| ZBR and ZRB add to 360º |
| What is known about angle MPC and MCP given that XC forms a tangent? |
| MPC and MCP add to 180º |
| MPC and MCP add to 90º |
| MPC is half MCP |
| MPC and MCP add to 360º |
| MPC is twice MCP |
| MPC is the same as MCP |