Mathematics
In △ABC, ∠B is a right angle. If D is the foot of the perpendicular drawn from B on AC, then:
BC2 + CD2 = AC2
AB2 - BC2 = AD2 - CD2
BC2 - BD2 = AB2 - AD2
None of these.
Answer
In △ ADB,
Using Pythagoras theorem,
Hypotenuse2 = Base2 + Height2
⇒ AB2 = BD2 + AD2
⇒ BD2 = AB2 - AD2 …..(1)
In △ BDC,
Using Pythagoras theorem,
⇒ BC2 = BD2 + CD2
⇒ BD2 = BC2 - CD2 ……(2)
Equating eq.(1) and (2), we get:
⇒ AB2 - AD2 = BC2 - CD2
⇒ AB2 - BC2 = AD2 - CD2.
Hence, option 2 is the correct option.
Related Questions
In △ABC, if AB = AC and D is a point on BC. Prove that AB2 - AD2 = BD × CD.
The lengths of the sides of some triangles in some unit are given below. Which of them is a right-angled triangle?
7, 9, 13
10, 24, 26
6, 8, 12
8, 12, 16
In the adjoining figure, CD =
36 cm
40 cm
41 cm
None of these
In the adjoining figure, AC =
17 cm
20 cm
22 cm
24 cm