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.