Question
Download Solution PDFA 15 cm long perpendicular is drawn from the centre of a circle to a 40 cm long chord. Find the diameter of the circle.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven :
A 15 cm long perpendicular is drawn from the centre of a circle to a 40 cm long chord
Concept used :
The line is drawn from the centre of a circle towards a chord always divides the chord in two equal parts and also perpendicular to the chord.
Calculations :
Let the centre of the circle be 'O' and 'OA' = OB is the radius
Let the chord be 'AB' where 'P' is the midpoint of the chord.
The length of chord AC is 40 cm so PA is equal to 20 cm
Now according to the question
OA2 = OP2 + PB2
OA2 = 152 + 202
OA2 = 225 + 400
OA2 = 625
⇒ OA = √625
⇒ 25
Now,
Diameter of the circle = 2 × Radius
⇒ 2 × 25
⇒ 50 cm
∴ The diameter of the circle is 50 cm.
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