10 concentric circles are drawn, with radii 1 cm, 2 cm, 3 cm, … , 10 cm. From a point P on the outermost circle, tangents are drawn to each of the inner circles. How many of these tangents have their lengths as integers?
Please help me with the steps and the solution
Answers
Given : 10 concentric circles are drawn, with radii 1 cm, 2 cm, 3 cm, … , 10 cm.
From a point P on the outermost circle, tangents are drawn to each of the inner circles.
To Find : How many of these tangents have their lengths as integers
Step-by-step explanation:
There will be two tangent at Each circle
Tangent length =
√10² - 1² , √10² - 2² , √10² - 3² , √10² - 4² , √10² - 5² , √10² - 6² , √10² - 7² , √10² - 8² , √10² - 9²
= √99 , √96 , √91 , √84 , √75 , √64 , √51 , √36 , √19
√64 = 8
√36 = 6
2 * 2 = 4 Tangents
4 tangents have their lengths as integers
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Answer:
Step-by-step explanation:
Given : 10 concentric circles are drawn, with radii 1 cm, 2 cm, 3 cm, … , 10 cm.
From a point P on the outermost circle, tangents are drawn to each of the inner circles.
To Find : How many of these tangents have their lengths as integers
Step-by-step explanation:
There will be two tangent at Each circle
Tangent length =
√10² - 1² , √10² - 2² , √10² - 3² , √10² - 4² , √10² - 5² , √10² - 6² , √10² - 7² , √10² - 8² , √10² - 9²
= √99 , √96 , √91 , √84 , √75 , √64 , √51 , √36 , √19
√64 = 8
√36 = 6
2 * 2 = 4 Tangents
4 tangents have their lengths as integers
Learn More:
In the given fig AM,ANand BC fare tangents to the circle find the ...
brainly.in/question/9909143
In the figure o is the center of circle.radius of circle is 3.1cm and pa is ...
brainly.in/question/7157405