sharmaramveer763
Answered

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Find the length of a chord which is at a distance of 4 cm from the centre of the circle of radius 6cm.​

Sagot :

semsee45

Answer:

4√5 cm

Step-by-step explanation:

Connect the two points at which the chord touches the circle to the center - these are radii.

We know that the chord is 4cm from the center of the circle.

So we now have an isosceles triangle with height of 4cm and congruent side lengths of 6cm (see attached diagram for visual representation). An isosceles triangle is made up of 2 congruent right triangles.

To find the length of the chord, all we have to do is calculate the shorter leg of one of the right triangles and multiply it by 2.

Use Pythagoras' Theorem:  a² + b² = c²

(where a and b are the legs and c is the hypotenuse of a right triangle).

Therefore, a² + 4² = 6²

                 a² + 16 = 36

                        a² = 36 - 16 = 20

                          a = √20 = 2√5

So the length of the chord = 2 x 2√5 = 4√5 cm

View image semsee45
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