Triangle ABC is such that AB = 16 cm, BC = 63 cm, AC = 65 cm. Do points A, B and C lie on the circumference of a circle? Explain with working. Answer ... ...

Right angled check Angle properties 中文

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1. Identify the longest side and test using Pythagoras' theorem

The longest side is $AC=65$ cm.

$16^2+63^2=256+3969=4225$

$65^2=4225$

2. Conclude that the triangle is right-angled

Since

$16^2+63^2=65^2,$

triangle $ABC$ is right-angled at $B$ .

3. Use the right angle to justify that the three points lie on a circle

A right angle is formed in a semicircle, so $AC$ can be the diameter of the circle and $B$ lies on its circumference.

Therefore, $A$ , $B$ and $C$ lie on the circumference of a circle.

Answer

Yes. Since $16^2+63^2=65^2$ , triangle $ABC$ is right-angled at $B$ . Hence $A$ , $B$ and $C$ lie on the circumference of a circle with $AC$ as diameter.

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Triangle ABC is such that AB = 16 cm, BC = 63 cm, AC = 65 cm. Do points A, B and C lie on the circumference of a circle? Explain with working. Answer ... ...

Worked solution

11

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