Question

triangle ABC is a right angle triangle in which angle C is 90°. if CD is perpendicular to AB and BC=a,CA=b,AB=c,CD=p prove that cp=ab and 1/p^2=1/a^2+1/b^2​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Area of ΔABC = (1/2) * AB * DC

                       = (1/2) * c * p

                       = cp/2

Again,

Area of ΔABC = (1/2) * AC * BC

                        = (1/2) * b * a

                        = (ab/2)

Comparing two above areas,

=> ab/2 = pc/2

=> ab = PC {Hence Proved}

Now,

In ΔABC,

AB² = BC² + AC²

=> c² = a² + b²

=> 1/p² = a^2 + b^2/a²b²{cp = ab and c = ab/p}

=> 1/p² = 1/a² + 1/b²[Hence Proved]

Hope it helps!