帮我解释一下这道题---**Question:** 2. 如图，⊙O的半径OA等于5，半径OC与弦AB垂直，垂足为D，若OD=3，则弦AB的长为（ ）
**Options:**
A. 10
B. 8
C. 6
D. 4
**Image Description:**
* **Type:** Geometric figure - Circle.
* **Main Elements:**
* A circle with center labeled O.
* Points A, B, C on the circle's circumference.
* Point D on the chord AB.
* Line segment OA (radius) is drawn.
* Line segment OC (radius) is drawn, passing through point D.
* Line segment AB (chord) is drawn.
* Line segment OD is drawn.
* There is a right angle symbol at point D, indicating that OC (and OD) is perpendicular to AB.
* Labels: O (center), A, B, C (on circle), D (intersection of OC and AB).
* Relative Position: O is the center. A, B, C are on the circle. D is on AB and on the line segment from O to C. OC is perpendicular to AB at D. OA is a radius.
**Relevant Information from Image/Text:**
* Circle with center O.
* Radius OA = 5.
* Radius OC is perpendicular to chord AB at point D.
* OD = 3.
* Find the length of chord AB.
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Let's analyze this circle geometry problem step by step. We have a circle with center O, where radius OA equals 5. The radius OC is perpendicular to chord AB at point D, and we know that OD equals 3. We need to find the length of chord AB.
Now let's apply a key property of circles. When a radius is perpendicular to a chord, it bisects that chord. Since radius OC is perpendicular to chord AB at point D, this means D is the midpoint of AB. Therefore, AD equals DB, and the chord is split into two equal segments.
Now we can apply the Pythagorean theorem to the right triangle ODA. We know that OA equals 5 as the radius, OD equals 3 as given, and we need to find AD. Using the theorem: OA squared equals OD squared plus AD squared. Substituting: 25 equals 9 plus AD squared, so AD squared equals 16, and therefore AD equals 4.
Now we can find the complete chord length. Since D is the midpoint of chord AB, and we found that AD equals 4, then DB also equals 4. Therefore, the total length of chord AB is AD plus DB, which equals 4 plus 4, giving us 8. The answer is B.
Let's summarize our solution. We used the key property that a perpendicular radius bisects a chord, applied the Pythagorean theorem to find AD equals 4, and then calculated the total chord length as 8. The correct answer is option B. This problem demonstrates important circle geometry concepts including perpendicular radius properties and the Pythagorean theorem.