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It looks like you've uploaded a page from a math workbook, which contains various geometry and algebra problems. Let's go over each part step-by-step. I'll address a few of the problems below.

### PART-B Problems:

1. **Question 13**: In the given triangle problem with a semicircular region, you need to find the area of the shaded region.
   - The triangle's dimensions are given, and you're expected to subtract the area of the semicircle from the area of the triangle.

2. **Question 14**: You need to **prove that the lengths of tangents drawn from an external point to a circle are equal**. This is a classic theorem from geometry related to tangents of a circle. The solution generally involves using the Pythagorean theorem and properties of tangents.

### Multiple Choice Questions:

1. **Question 1**: Which quadratic equation has equal roots? 
   - Roots are equal if the discriminant \( b^2 - 4ac = 0 \). Solve this for the equations.

2. **Question 2**: The length of a tangent to a circle from a point outside the circle.
   - You can use the Pythagorean theorem for tangents to solve this, where the tangent is the perpendicular distance.

3. **Question 5**: A line intersecting a circle in two points is called:
   - This is a **secant** of the circle.

4. **Question 8**: Find the ratio in which the Y-axis divides the line segment joining two points.
   - Use section formula to calculate the ratio.

5. **Question 10**: Tangents drawn at the end points of a diameter are...?
   - These are **parallel**.

Let me know which specific question you'd like a detailed solution for, or if you'd like to dive into any particular problem! 

### Expanding the Learning:
Here are 5 related questions you might find useful to explore:
1. How can you derive the area of a triangle using the coordinates of its vertices?
2. What is the significance of the discriminant in quadratic equations?
3. How do you calculate the length of a tangent from an external point to a circle?
4. What are the different types of lines that can intersect or touch a circle, and how do they differ?
5. How do you prove that two tangents from a point to a circle are of equal length?

**Tip**: When working with geometry, always draw a clear diagram and label all known values to visualize the problem better.

Various geometry and algebra questions related to tangents, triangles, and circles.

This page contains solutions to a variety of geometry and algebra problems, including finding the area of a shaded region, proving tangent properties, and solving quadratic equations. Suitable for Grade 10 students.

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