Chapter 9: Q18. (page 331)

Drawtwo congruent circles with radii $6$ each passing through the centre of other and to find length of their common chord.

Short Answer

Expert verified

$6 \sqrt{3}$

Step by step solution

Step 1. Given information.

Radii of both the circles are $6$ and they pass through the centre of each other.

Step 2. Concept used.

Perpendicular from centre of circle to the chord bisects he chord.

Step 3. Solution.

Two circles can be drawn as:

To find the length of the common chord $A B i n Δ ADC$ :

$\begin{matrix} A D = \sqrt{A C^{2} + C D^{2}} \\ A D = \sqrt{A C^{2} + {(\frac{D E}{2})}^{2}} \\ 6 = \sqrt{A C^{2} + {(\frac{6}{2})}^{2}} \\ 6^{2} = A C^{2} + {(\frac{6}{2})}^{2} \\ 36 = A C^{2} + 9 \\ A C^{2} = 27 \\ A C = \sqrt{27} \\ A C = 3 \sqrt{3} \end{matrix}$

Perpendicular to any chord bisects the chord therefore,

$\begin{array}{l} A B = 2 A C \\ A B = 2 \times (3 \sqrt{3}) \\ A B = 6 \sqrt{3} \end{array}$

Therefore, the answer is $6 \sqrt{3}$ .

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Drawtwo congruent circles with radii $6$ each passing through the centre of other and to find length of their common chord.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Solution.

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Drawtwo congruent circles with radii 6 each passing through the centre of other and to find length of their common chord.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Geometry

Pure Maths

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Drawtwo congruent circles with radii $6$ each passing through the centre of other and to find length of their common chord.