Answered: "AB is diameter whose center is O of..."

Vagotonusybk

Answered question

2022-02-09

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

Nathan Huang

Beginner2022-02-10Added 15 answers

Step 1

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

∠ A C B

is a right angle.
Given AB is a diameter, and

A C = 3

, and

B C = 4

\Rightarrow ∠ A C B = 90^{\circ}

by Pythagorean theorem,

A B^{2} = A C^{2} + B C^{2}

\Rightarrow A B^{2} = 3^{2} + 4^{2} = 25

\Rightarrow A B = \sqrt{25} = 5

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