Advertisements
Advertisements
प्रश्न
The perpendicular from A on side BC of a Δ ABC intersects BC at D such that DB = 3CD . Prove that 2AB2 = 2AC2 + BC2.
उत्तर
Applying Pythagoras theorem for ΔACD, we obtain
AC2 = AD2 +DC2
AD2 = AC2 - DC2 ... (1)
Applying Pythagoras theorem in ΔABD, we obtain
AB2 = AD2 + DB2
AD2 = AB2 - DB2 ...(2)
From equation 1 and 2 we obtain
AC2 - DC2 = AB2 - DB2 ....(3)
it is given that 3DC = DB
`:.DC = (BC)/4 `
Putting these value in equation 3 we obtain
`(AC)^2 - ((BC)/4) ^2 = (AB)^2 - ((3BC)/4)^2`
`(AC)^2 - (BC)^2/16 = (AB)^2-`
16AC2 - BC2 = 16AB2 - 9BC2
16AB2 - 16AC2 8BC2
2AB2 = 2AC2 + BC2
APPEARS IN
संबंधित प्रश्न
In Fig., ∆ABC is an obtuse triangle, obtuse angled at B. If AD ⊥ CB, prove that AC2 = AB2 + BC2 + 2BC × BD
In a ∆ABC, AD ⊥ BC and AD2 = BC × CD. Prove ∆ABC is a right triangle
Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.
Find the Pythagorean triplet from among the following set of numbers.
9, 40, 41
The sides of the triangle are given below. Find out which one is the right-angled triangle?
8, 15, 17
The sides of the triangle are given below. Find out which one is the right-angled triangle?
11, 60, 61
A right triangle has hypotenuse p cm and one side q cm. If p - q = 1, find the length of third side of the triangle.
There are two paths that one can choose to go from Sarah’s house to James's house. One way is to take C street, and the other way requires to take B street and then A street. How much shorter is the direct path along C street?
In the adjoining figure, a tangent is drawn to a circle of radius 4 cm and centre C, at the point S. Find the length of the tangent ST, if CT = 10 cm.
A right-angled triangle may have all sides equal.
