Two circles of equal radii touch each other at point D(p,p).Centre A of the one circle lies on the Y-axis.Point B(8,7) is the centre of the other circle.FDE is a common tangent to both circles

Here's how to approach this problem and the information we can determine: **Visualization** Imagine two circles touching at a single point (D). Since they have equal radii, the line connecting their centers (A and B) will pass through their point of contact (D). **Key Information:** * **Centers:** A (0, y) on the y-axis, and B (8, 7) * **Tangent:** FDE is a common tangent, meaning it touches both circles at a single point each (F and E). **What we can find:** 1. **Coordinates of D:** Since D is the midpoint of line segment AB, we can use the midpoint formula: * D = ((0 + 8)/2, (y + 7)/2) = (4, (y+7)/2) * We also know that D has coordinates (p, p). Therefore, p = 4 and (y+7)/2 = p =4 * Solving for y, we get y = 1. * So, D has coordinates (4, 4). 2. **Radius of the circles:** We can find the radius by calculating the distance between the centers (A or B) and point D, using the distance formula. 3. **Equations of the Circles:** With the centers and radius known, we can use the standard equation of a circle: * Circle A: (x - 0)² + (y - 1)² = radius² * Circle B: (x - 8)² + (y - 7)² = radius² **Can't Determine Without More Info:** * **Equations of the tangent FDE:** We need at least one point (F or E) on the tangent, or its slope, to find its equation. **Let me know if you have more information on the tangent, and I can help you find its equation!**