Question

Two concentric circles are of radii 5cm and 3cm. Find the length of of the chord of the larger circle which touches the smaller circle.​

Answer 1

$\color{red}\huge{\underline{\underline{GIVEN\dag}}}$

• Radii of small circle=3cm
• Radii of large circle=5cm

$\color{red}\huge{\underline{\underline{TO\:FIND\dag}}}$

• Chord AB

$\color{red}\huge{\underline{\underline{SOLUTION\dag}}}$

By pythagoras theorem;

$(OA)^{2}=(AC)^{2}+(OC)^{2}$

$5^{2}=AC^{2}+3^{2}$

$25=AC^{2}+9$

$AC^{2}=25-9$

$AC^{2}=16$

$AC=\sqrt{16}$

$\therefore AC=4cm$

Similarly;

$CB=4cm$

BUT;

length of chord equals to AB

$AB=AC+CB$

$\implies AB=4cm+8cm$

$\orange{\boxed{\therefore AB=4cm+8cm}}$

Therefore,

Length of chord is "8cm".

HOPE THAT HELPS!!