AD is a diameter of a circle and AB is a chord. If AD = 26 cm, AB = 10 cm, find the perpendicular distance of AB from the centre of the circle.
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Step by Step Explanation:
- Let us draw the figure as follows:
We are told that the diameter AD = 26 cm and the length of the chord AB = 10 cm.
We are asked to find the perpendicular distance of AB from the center O.
This is the length of the line segment OC.
- We can see that △OAC is a right-angled triangle.
We also know that OA is the radius, i.e half of the diameter AD.
Therefore, AO = 13 cm.
- We know that the perpendicular to the chord from the center i.e. OC, divides the chord into two equal parts.
Therefore, AC = CB = = = 5 cm
- Since, △OAC is a right angle triangle, OC2 + AC2 = OA2
⇒ OC2 + 52 = 132
⇒ OC2 = 169 - 25
⇒ OC2 = 144
⇒ OC = 12 cm
- Therefore, perpendicular distance of AB from the centre of the circle is 12 cm.