SSC CGL 7 06 2019 Shift 1 Paper

Question : 61 of 100

Marks: +1, -0

Two chords AB and CD of lengths 5cm and 11 cm respectively are parallel and are on the same side of the centre 0 of a circle. If the distance between the chords is 3 cm, then what is the diameter of the circle?

37 cm
$√146$ cm
$√142$ cm
38 cm

Validate

Solution:

Let radius = rIn

\Δ {OQD}

\ {OQ}^{2}=\ {r}^{2}-\ (\ {11}/{2}\ )^{2}

O Q=\√{r^{2}-\ (\ {11}/{2}\ )^{2}}

Also

\ {OP}=\√{r^{2}-\ (\ {5}/{2}\ )^{2}}

\ {\Now}, \ {OP}-\ {OQ}=3

\⇒ \√{r^{2}-\ (\ {5}/{2}\ )^{2}}

-\√{r^{2}-\ (\ {11}/{2}\ )^{2}}=3

\⇒r^{2}-\ ( {5}/{2}\ )^{2}=9+\ [r^{2}-\ (\ {11}/{2}\ )^{2}\ ]

-6 \√{r^{2}-\ (\ {11}/{2}\ )^{2}}

\⇒6 \√{r^{2}-\ (\ {11}/{2}\ )^{2}}

=9-\ {121}/{4}+\ {25}/{4}

\⇒r^{2}-\ (\ {11}/{2}\ )^{2}=\ {225}/{36}

\⇒r^{2}=\ {225}/{36}+\ {121}/{4}

\⇒r=\√{36.5}

Diameter

=2 r=\√{4 \ ×36.5}=\√{146}

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