Answer:
Step-by-step explanation:
9). "Tangent is perpendicular to the radius of a circle"
By applying Pythagoras theorem in the given triangle,
x² = 15² + 20²
x = √625 = 25
10). By applying Pythagoras theorem in the given triangle,
(r + x)² = r² + 15²
(8 + x)² = 8² + 225
8² + x² + 16x = 8² + 225
x² + 16x = 225
x² + 16x - 225 = 0
x² + 25x - 9x - 225 = 0
x(x + 25) - 9(x + 25) = 0
(x + 25)(x - 9) = 0
x = -25, 9
But x > 0
Therefore, x = 9 is the answer.
11). By the property of the tangents drawn to the circle from a point,
"Tangents drawn from a point lying outside the circle are equal in measure"
AC = BC
3x + 4 = 40
3x = 36
x = 12
12). By the same property used in question (11)
DE = DC = 4 units
BA = BC = 3 units
x = 4 + 3 = 7 units
