The height CD, drawn to the base AB of an isosceles triangle ABC, is 3 cm, AB = 8 cm.

| June 17, 2021 | education

The height CD, drawn to the base AB of an isosceles triangle ABC, is 3 cm, AB = 8 cm. Find the radii of the circles inscribed in the triangle and circumscribed around the triangle.

Since triangle ABC is isosceles, then its height CD is also its median, then AD = BD = AB / 2 = 8/2 = 4 cm.

In a right-angled triangle ACD, according to the Pythagorean theorem, AC ^ 2 = AD ^ 2 + CD ^ 2 = 16 + 9 = 25.

AC = 5 cm.

Determine the area of the triangle ABC. Savs = AB * CD / 2 = 8 * 3/2 = 12 cm2.

The radius of the circumscribed circle is equal to: R = AB * AC * BC / 4 * Savs = 8 * 5 * 5/4 * 12 = 200/48 = 25/6 = 4 (1/6) cm.

The radius of the inscribed circle is: r = 2 * Savs / (AB + AC + BC) = 2 * 12/18 = 2/3 cm.

Answer: The radius of the inscribed circle is 2/3 cm, the radius of the inscribed circle is 4 (1/6) cm.



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