A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
In the given figure, ΔABC is an obtuse triangle, obtuse angled at B. If AD⊥CB , then prove that AC2 = AB2 + BC2 + 2BC.BD
Solution:
From the right angled triangle ADC,
Using pythagoras theorem, AD2 + DC2 = AC2 --- (1)
From the figure,
DC = DB +BC --- (2)
Substitute DC from (2) in equation (1)
AD2 + (BD + BC)2 = AC2
AC2 = AD2 + BD2 + BC2 + 2BD.BC --- (3)
Also from right angled triangle ADB,
AD2 + BD2 = AB2 (From pythagoras theorem) --- (4)
Substitute (4) in equation (3)
AC2 = AB2 + BC2 + 2BD.BC
In the given figure, ΔABC is an obtuse triangle, obtuse angled at B. If AD⊥CB , then prove that AC2 = AB2 + BC2 + 2BC.BD ?
Summary:
Given ΔABC is an obtuse triangle, obtuse angled at B and AD⊥CB, then AC2 = AB2 + BC2 + 2BC.BD.
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