The perpendicular distance from the center of a circle to the chord is 20 cm. Calculate the chord's length in centimeters if the circle's diameter is 58 cm.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 42.
Here,
OA is the radius
OA = Diameter/2
⇒ OA = 58/2 = 29 cm
⇒ OD = 20 cm
In △ODA
⇒ OA2 = OD2 + DA2
⇒ 292 = 202 + DA2
⇒ DA2 = 841 - 400
⇒ DA2 = 441
⇒ DA = 21 cm
Thus, AB = 2 × DA
⇒ AB = 2 × 21 = 42 cm