In the R T triangle AOB, ∠ o = 90 degrees, OA = 6, OB = 8, take o as the center of the circle, OA as the radius, make the circle AB to C, and find the length of BC?

In the R T triangle AOB, ∠ o = 90 degrees, OA = 6, OB = 8, take o as the center of the circle, OA as the radius, make the circle AB to C, and find the length of BC?

According to Pythagorean theorem, we can find the hypotenuse AB = √ (OA & sup2 + ob & sup2) = √ (6 & sup2 + 8 & sup2) = 10 in RT △ AOB. In addition, according to the area of RT △ AOC, we can get the height h = 2S / AB = OA · ob / AB = 4.8
When ⊙ o intersects AB with C with OA as radius, △ AOC is an isosceles triangle, and the height of the bottom edge is h like RT △ AOB, so the bottom edge length AC = 2 × √ (OA & sup2-h & sup2) = 2 × √ (6 & sup2-4.8 & sup2) = 2 × 3.6 = 7.2, so BC = AB-AC = 10-7.2 = 2.8