Question

Geometry pls help !!! Find the value of AB.
AB = [?]

Answer 1

AB = 16 Units

Explanation:

In the given figure, CD is the diameter and AB is the chord of the circle.

Since, diameter of the circle bisects the chord at right angle.

Therefore, AE = 1/2 AB

Or AB = 2AE...(1)

Let the center of the circle be given by O. Join OA.

OA = OD = 10 (Radii of same circle)

Triangle OAE is right triangle.

Now, by Pythagoras theorem:

`OA^2 = AE^2 + OE^2 \\</p><p>10^2 = AE^2 + 6^2 \\</p><p>100= AE^2 + 36\\</p><p>100-36 = AE^2 \\</p><p>64= AE^2 \\</p><p>AE = √(64)\\</p><p>AE = 8 \\</p><p>\because AB = 2AE..[From \: equation\: (1)] \\</p><p>\therefore AB = 2* 8\\</p><p>\huge \purple {\boxed {AB = 16 \: Units}}`