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The Length of Common Chord of Two Intersecting Circles is 30 Cm. If the Diameters of These Two Circles Be 50 Cm and 34 Cm, Calculate the Distance Between Their Centres. - ICSE Class 10 - Mathematics

ConceptChord Properties - a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord

Question

The length of common chord of two intersecting circles is 30 cm. If the diameters of these two circles be 50 cm and 34 cm, calculate the distance between their centres.

Solution OA = 25 cm and AB = 30 cm

∴ AD = 1/2× AB =(1/2×30)cm = 15 cm

Now in right angled ΔADO,

OA^2 = AD^2 + OD^2
⇒ OD^2 = OA^2 - OD^2 = 25^2 -15^2
= 625 - 225 = 400

∴ OD =sqrt 400 = 20 cm
Again, we have O 'A = 17 cm
In right angle ΔADO'
 O'A ^2= AD^2 +O'D^2
⇒ O'D^2 =O'A^2 - AD^2 = 17^2 -15^2
⇒ 289 - 225 = 64
∴ O'D 8 cm
∴ OO' (OD+ O'D)
= (20 +8)= 28 cm
∴ the distance between their centres is 28 cm

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Solution The Length of Common Chord of Two Intersecting Circles is 30 Cm. If the Diameters of These Two Circles Be 50 Cm and 34 Cm, Calculate the Distance Between Their Centres. Concept: Chord Properties - a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord.
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