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AB is diameter whose center is O of a circle. If AC is 3 cm and BC is 4 cm, then find AB?

Answer 1

#AB=5#

I have to assume point #C# is on the circle too.

In geometry, if #A,B and C# are points on a circle when the line #AB# is a diameter of the circle, then #angleACB# is a right angle.

Given #AB# is a diameter, and #AC=3, and BC=4#,
#=> angleACB=90^@#
by Pythagorean theorem,
#AB^2=AC^2+BC^2#
#=> AB^2=3^2+4^2=25#
#=> AB=sqrt25=5#

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Answer 2

Carson Arnold

Since AB is the diameter of the circle, it is twice the radius of the circle. Therefore, AB = 2 * radius. The radius of the circle is half of the diameter, so if AC and BC are the legs of a right triangle, with AC being 3 cm and BC being 4 cm, then using the Pythagorean theorem, we can find the length of AB.

[AB^2 = AC^2 + BC^2]

[AB^2 = 3^2 + 4^2]

[AB^2 = 9 + 16]

[AB^2 = 25]

[AB = \sqrt{25}]

[AB = 5]

Therefore, the length of AB, the diameter of the circle, is 5 cm.

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Answer from HIX Tutor

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