Question
Download Solution PDFIf the length of a chord, drawn at a distance of 21 cm from the centre of a circle, is 40 cm, then the radius (in cm) of the circle is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Chord = 40cm
Distance from centre to chord = 21 cm
Concept:
The perpendicular drawn from the centre of the chord bisects the chord in two equal parts.
Pythagoras Theorem:
OA2 = OD2 + AD2
Calculation:
Let AB be the chord of length 40 cm.
⇒ OD be the perpendicular distance
⇒ AO be the radius of the circle
OA2 = OD2 + AD2
⇒ OA2 = 212 + (40/2)2
⇒ OA2 = 441 + 400
⇒ OA2= 841
OA = √841
OA = 29
The radius (in cm) of the circle is 29.
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