Get the solution to "Two circles intersesct and have a common chord..."

jernplate8

Answered question

2021-08-14

Two circles intersesct and have a common chord 12 cm long.

tabuordg

Skilled2021-08-15Added 99 answers

the problem solved in this way

2021-12-24

Step 1

Given

Two circles (say) $O_{1}$ and $O_{2}$ intersect and have a common chord say (AB) of 12 cm long.

Angle of Point of intersection is $45^{\circ}$

To find:

Length of radius of each circle

Trigonometric identities

$\sin θ = \frac{opposite side}{Hypotenuse side}$

Step 2

Consider the triangle $A O_{1} O_{2}$ from circles

From chord AB, AN=6

Also $θ = 45^{\circ}$

Now

$\sin 45^{\circ} = \frac{6}{radius of O_{1}}$

$\frac{1}{\sqrt{2}} = \frac{6}{r}$

$r = 6 \sqrt{2}$

By similar argument

Radius of $O_{2} = 6 \sqrt{2}$

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