Advertisements
Advertisements
प्रश्न
In the following figure, AD is perpendicular to BC and D divides BC in the ratio 1: 3.
Prove that : 2AC2 = 2AB2 + BC2
Advertisements
उत्तर
Here,
BD : DC = 1 : 3.
⇒ BD = `1/4"BC" and CD = 3/4`BC
AC2 = AD2 + CD2 and AB2 = AD2 + BD2
Therefore,
AC2 - AB2 = CD2 - BD2
= `( 3/4"BC" )^2 - ( 1/4 "BC" )^2 `
= `9/16 "BC"^2 - 1/16 "BC"^2`
= `1/2"BC"^2`
∴ 2AC2 - 2AB2 = BC2
2AC2 = 2AB2 + BC2
Hence proved.
APPEARS IN
संबंधित 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.
In the given figure, M is the midpoint of QR. ∠PRQ = 90°. Prove that, PQ2 = 4PM2 – 3PR2.
In ∆ABC, ∠BAC = 90°, seg BL and seg CM are medians of ∆ABC. Then prove that:
4(BL2 + CM2) = 5 BC2
In triangle ABC, AB = AC = x, BC = 10 cm and the area of the triangle is 60 cm2.
Find x.
In an isosceles triangle ABC; AB = AC and D is the point on BC produced.
Prove that: AD2 = AC2 + BD.CD.
In Fig. 3, ∠ACB = 90° and CD ⊥ AB, prove that CD2 = BD x AD.
In triangle PQR, angle Q = 90°, find: PR, if PQ = 8 cm and QR = 6 cm
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 = AD2 + BC x DE + `(1)/(4)"BC"^2`
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 + AC2 = 2AD2 + `(1)/(2)"BC"^2`
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 + AC2 = 2(AD2 + CD2)
In a right angled triangle, the hypotenuse is the greatest side
Find the unknown side in the following triangles
Find the unknown side in the following triangles
Find the length of the support cable required to support the tower with the floor
Choose the correct alternative:
If length of sides of a triangle are a, b, c and a2 + b2 = c2, then which type of triangle it is?
The longest side of a right angled triangle is called its ______.
Two squares having same perimeter are congruent.
If two legs of a right triangle are equal to two legs of another right triangle, then the right triangles are congruent.
The hypotenuse (in cm) of a right angled triangle is 6 cm more than twice the length of the shortest side. If the length of third side is 6 cm less than thrice the length of shortest side, then find the dimensions of the triangle.
