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Area of Square

Two concentri...

Question

Two concentric circles with centre $O$ have $A, B, C, D$ as the points of intersection with the line $l$ as shown in the figure. If $A D = 12 c m$ and $B C = 8$ cm, the length of $A B, C D, A C$ and $B D$ are respectively.

2

cm,

2

cm,

10

cm,

10

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10

cm,

10

cm,

2

cm,

2

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10

cm,

2

cm,

10

cm,

2

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2

cm,

10

cm,

2

cm,

10

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct option is A $2$ cm, $2$ cm, $10$ cm, $10$ cm
Draw $a ⊥ O M$ to $l$

$O M ⊥ B C a n d O M ⊥ A D$

We know that perpendicular lines to a chord which pass through center bisect the chord

$⟹ B M = M C = \frac{1}{2} B C = 4 c m$

$⟹ A M = M D = \frac{1}{2} A D = 6 c m$

$A B = C D = A M - B M = 6 - 4 = 2 c m$

$A C = B D = A B + B C = 2 + 8 = 10 c m$

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Two concentric circles with centre O have A,B,C,D as the points of intersection with the line l as shown in the figure. If AD=12cm and BC=8 cm, the length of AB,CD,AC and BD are respectively.

The correct option is A 2 cm, 2 cm, 10 cm, 10 cmDraw a⊥OM to l OM⊥BCandOM⊥AD We know that perpendicular lines to a chord which pass through center bisect the chord ⟹BM=MC=12BC=4 cm ⟹AM=MD=12AD=6 cm AB=CD=AM–BM=6–4=2 cm AC=BD=AB+BC=2+8=10 cm

Two concentric circles with centre $O$ have $A, B, C, D$ as the points of intersection with the line $l$ as shown in the figure. If $A D = 12 c m$ and $B C = 8$ cm, the length of $A B, C D, A C$ and $B D$ are respectively.