Unit 10 Tangent to a Circle Step-by-step Solutions
Welcome to the solutions for Unit 10 Tangent to a Circle! This unit covers essential theorems and concepts related to tangents and their relationship with circles. Mastering these key points is crucial for solving problems that involve tangents, radii, and circle geometry. Whether you’re reviewing the basics or tackling challenging exercises, this post provides detailed solutions and clear explanations to help you understand every part of this unit. If you’d like to download the PDF solutions, simply click on the arrow in the top-right corner of the embedded PDF, and it will open in a new window where the download option will appear.
PDF Solutions
Multiple Choice Questions Test for Unit 10
To reinforce your learning, we’ve included an interactive MCQ test for Unit 10 Tangent to a Circle. This test allows you to assess your understanding of the concepts and practice applying the theorems and proofs you’ve studied. Simply click on the “Start Test” button to begin, and use it as a tool to check your progress and boost your confidence. It’s a great way to test your knowledge before moving on to the next topic.
Unit 10 Tangent to a Circle Key Points
- Line Perpendicular to a Radial Segment is Tangent:
- Statement: A line drawn perpendicular to a radial segment of a circle at its outer end point is tangent to the circle at that point.
- Proof: If a line is perpendicular to the radius at the outer end, it will only touch the circle at that point and not cross it. Therefore, it’s a tangent.
2. Tangent and Radius are Perpendicular:
- Statement: The tangent to a circle at any point is perpendicular to the radius drawn to that point of contact.
- Proof: By definition, a tangent to a circle is a line that touches the circle at exactly one point, and at this point, the radius is perpendicular to the tangent.
3. Two Tangents from an External Point:
- Statement: The lengths of two tangents drawn from an external point to a circle are equal.
- Proof: The tangents from an external point to a circle are equal because they form two congruent right triangles with the radius and the line segment connecting the external point to the circle’s center.
4. Distance Between Centers of Touching Circles:
- Statement: For two circles touching externally, the distance between their centers is equal to the sum of their radii. For circles touching internally, the distance is equal to the difference of their radii.
- Proof: If two circles touch externally, their centers are separated by a distance equal to the sum of their radii. If they touch internally, the distance between their centers is the difference of their radii.
This post provides a comprehensive guide for Unit 10 Tangent to a Circle, including the key points, detailed PDF solutions for each exercise, and an MCQ test to test your skills. By working through the solutions and reviewing the key theorems, you’ll be better equipped to handle problems on tangents and circles. Be sure to explore each section thoroughly to gain a deeper understanding and prepare effectively for your exams. This Video Lecture of Unit 10 will further help you understand the concepts.
Have a look at important Formulas Used in this Unit 10.
With a solid grasp of Unit 10 Tangent to a Circle, you’re now well-prepared to build on these foundational concepts. Tangents play an important role in understanding more advanced topics in geometry, and the practice you’ve done here will make those upcoming challenges easier to tackle. Now, let’s move on to Unit 11 Solutions, where we’ll explore chords, arcs, and their unique properties within circles. Dive in and continue strengthening your knowledge step-by-step!