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 DMC and DCM given that PC 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 BRZ and BZR given that PZ forms a tangent? |
| BRZ and BZR add to 180º |
| BRZ is half BZR |
| BRZ and BZR add to 360º |
| BRZ is twice BZR |
| BRZ and BZR add to 90º |
| BRZ is the same as BZR |
| What is known about angle YCM and YMC given that BM forms a tangent? |
| YCM and YMC add to 180º |
| YCM is half YMC |
| YCM and YMC add to 360º |
| YCM and YMC add to 90º |
| YCM is twice YMC |
| YCM is the same as YMC |
| What is known about angle YDZ and YZD given that XZ forms a tangent? |
| YDZ and YZD add to 90º |
| YDZ is the same as YZD |
| Nothing, YDZ and YZD are not subtended by the same arc |
| YDZ is twice YZD |
| YDZ and YZD add to 180º |
| YDZ is half YZD |
| What is known about angle BDC and BCD given that YC forms a tangent? |
| BDC is the same as BCD |
| BDC is half BCD |
| BDC and BCD add to 360º |
| BDC and BCD add to 90º |
| Nothing, BDC and BCD are not subtended by the same arc |
| BDC and BCD add to 180º |
| What is known about angle CPR and CRP given that NR forms a tangent? |
| CPR and CRP add to 90º |
| CPR is the same as CRP |
| Nothing, CPR and CRP are not subtended by the same arc |
| CPR is half CRP |
| CPR is twice CRP |
| CPR and CRP add to 360º |
| What is known about angle MPC and MCP given that XC forms a tangent? |
| MPC and MCP add to 180º |
| MPC is half MCP |
| MPC and MCP add to 90º |
| MPC and MCP add to 360º |
| MPC is twice MCP |
| MPC is the same as MCP |
| What is known about angle ZBR and ZRB given that CR forms a tangent? |
| ZBR and ZRB add to 360º |
| Nothing, ZBR and ZRB are not subtended by the same arc |
| ZBR and ZRB add to 180º |
| ZBR and ZRB add to 90º |
| ZBR is half ZRB |
| ZBR is the same as ZRB |