Final Answer:
In a figure two chords are there AC and DF, AC = 22.5 and DF = 2b, two equal perpendiculars measuring 12 are drawn from the center to the chords, the value of b is 11.5, so the correct option is D.
Step-by-step explanation:
Let's solve the question step by step.
1. By property of circles, if two chords are of equal length, then their perpendicular distances from the center of the circle are also equal.
Conversely, if their perpendicular distances from the center of the circle are equal, then the chords themselves are of equal length.
Since it is given in the problem that the perpendicular distances from the center to both chords AC and DF are equal (12 units each), we can infer that the lengths of the chords AC and DF are also equal.
2. Given AC = 22.5 units, and since AC = DF (from the property mentioned above), we can say that DF also equals 22.5 units.
3. DF is given as 2b in the problem. Since we have established that DF equals 22.5 units, we can set up the following equation:
DF = 2b
22.5 = 2b
4. To find the value of b, we divide both sides of the equation by 2:
22.5 / 2 = 2b / 2
11.25 = b
Thus, the value of b is 11.25, so the correct option is D.