Let triangle ABC be a right triangle such that B is at the right angle. A circle with a diameter of BC meets side AC at D. If the area of triangle ABC is 150 and AC=25 then what is BD?

(no visual given)

SydSu22 Apr 10, 2019

#3**+1 **

OK....I think I have it.....letting BC = 15 and and BA = 20

Then AC = 25

And the product of the legs BC * BA / 2 = the area = 150

The circle is centered at (0, 7.5) and has a radius of 7.5

Notice in the diagram....angle ADB = 90°.....so BD is an altitude of triangle ABC

So...letting AC be a base...we have that

Area of ABC = (1/2) base * altitude

150 = (1/2)AC * ( BD)

150 = (1/2)AC * BD

150 = (1/2)(25) (BD)

300 = 25 (BD)

300 /25 = BD = 12

CPhill Apr 10, 2019