A triangle with a radius of 10 cm is inscribed in a circle, one side of which is the diameter. the other side of the triangle is 16 cm find the area of the triangle
1. ΔАВС – rectangular, since one of its sides (AB) is the diameter of the circumscribed circle. The side being the diameter is the hypotenuse.
Therefore AC and BC are ΔABC legs.
2.AB = R x 2 = 10 x 2 = 20 cm.
3. ВС = √АВ²-АС² (by the Pythagorean theorem).
BC = √20²- 16² = √400 – 256 = √144 = 12 cm.
4. Calculate the area (S) ΔАВС:
S = BC x AC: 2 = 12 x 16: 2 = 96 cm².
Answer: S ΔABC is equal to 96 cm².
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