If the angle of intersection at a point where the two circles with radii $5 c m$ and $12 c m$ intersect is $90 °,$ then the length $(in c m)$ of their common chord is :

\frac{120}{13}

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\frac{13}{2}

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\frac{60}{13}

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\frac{13}{5}

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Solution

The correct option is A $\frac{120}{13}$
Length of $C_{1} C_{2} = \sqrt{12^{2} + 5^{2}} = 13 c m$
As both the radii intersect is $90 ° \Rightarrow ∠ A = ∠ B = 90 °$
In $△ A C_{1} C_{2}$
Area $Δ = \frac{1}{2} \cdot A C_{1} \cdot A C_{2} = \frac{1}{2} \cdot 12 \cdot 5 = 30 c m$
Also $Δ = 30 = \frac{1}{2} \cdot A O \cdot 13$
$\Rightarrow A O = \frac{60}{13} c m$
$∴$ Length of common chord $A B = 2 \cdot A O = \frac{120}{13} c m$

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If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90°, then the length ( in cm) of their common chord is :

The correct option is A 12013Length of C1C2=√122+52=13 cm As both the radii intersect is 90°⇒∠A=∠B=90° In △AC1C2 Area Δ=12⋅AC1⋅AC2 =12⋅12⋅5=30 cm Also Δ=30=12⋅AO⋅13 ⇒AO=6013 cm ∴ Length of common chord AB=2⋅AO=12013 cm

If the angle of intersection at a point where the two circles with radii $5 c m$ and $12 c m$ intersect is $90 °,$ then the length $(in c m)$ of their common chord is :