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icang [17]
3 years ago
12

1. A chord is 22 cm long. It is 60 cm from the center of the circle.

Mathematics
1 answer:
mezya [45]3 years ago
3 0

Answer:

Radius, r = 61 cm

Step-by-step explanation:

According to the attached figure, we have,

Length of chord, AB = 22 cm

Such that, AP = PB = 11 cm

OP = 60 cm

It is required to find the radius of the circle. We know that radius of a circle is perpendicular to chord. So, APO forms a right angled triangle. Using Pythagoras theorem to find the radius of circle. Let it is r. So,

r^2=60^2+11^2\\\\r=61\ cm

So, the radius of the circle is 61 cm.

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kicyunya [14]

Consider the lengths of consecutive 1-2 blocks.

block 1 - 1, 2 - length 2

block 2 - 1, 2, 2 - length 3

block 3 - 1, 2, 2, 2 - length 4

block 4 - 1, 2, 2, 2, 2 - length 5

and so on.


Recall the formula for the sum of consecutive positive integers,

\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2

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In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of

\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224

numbers, and their sum is

\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400

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5 0
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