Advertisements
Advertisements
Question
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 - AB2 = 2BC x ED
Advertisements
Solution
We have ∠AED = 90°
∴ ∠ADE < 90° and ∠ADC > 90°
i.e. ∠ADE is acute and ∠ADC is obtuse.
Subtracting (ii) from (i), we have
AC2 - AB2 = AD2 + BC x DE + `(1)/(4)"BC"^2 - "AD"^2 + "BC" xx "DE" - (1)/(4)"BC"^2`
⇒ AC2 - AB2 = 2BC x DE.
APPEARS IN
RELATED QUESTIONS
In triangle ABC, ∠C=90°. Let BC= a, CA= b, AB= c and let 'p' be the length of the perpendicular from 'C' on AB, prove that:
1. cp = ab
2. `1/p^2=1/a^2+1/b^2`
A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?
In the given figure, ABC is a triangle in which ∠ABC < 90° and AD ⊥ BC. Prove that AC2 = AB2 + BC2 − 2BC.BD.
In the given figure, point T is in the interior of rectangle PQRS, Prove that, TS2 + TQ2 = TP2 + TR2 (As shown in the figure, draw seg AB || side SR and A-T-B)
Pranali and Prasad started walking to the East and to the North respectively, from the same point and at the same speed. After 2 hours distance between them was \[15\sqrt{2}\]
km. Find their speed per hour.
In a trapezium ABCD, seg AB || seg DC seg BD ⊥ seg AD, seg AC ⊥ seg BC, If AD = 15, BC = 15 and AB = 25. Find A(▢ABCD)
In right angle ΔABC, if ∠B = 90°, AB = 6, BC = 8, then find AC.
A man goes 40 m due north and then 50 m due west. Find his distance from the starting point.
In the given figure, ∠B = 90°, XY || BC, AB = 12 cm, AY = 8cm and AX : XB = 1 : 2 = AY : YC.
Find the lengths of AC and BC.
In triangle ABC, AB = AC = x, BC = 10 cm and the area of the triangle is 60 cm2.
Find x.
Find the value of (sin2 33 + sin2 57°)
Prove that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.
In the given figure, angle ADB = 90°, AC = AB = 26 cm and BD = DC. If the length of AD = 24 cm; find the length of BC.
A man goes 10 m due east and then 24 m due north. Find the distance from the straight point.
AD is perpendicular to the side BC of an equilateral ΔABC. Prove that 4AD2 = 3AB2.
In the given figure, PQ = `"RS"/(3)` = 8cm, 3ST = 4QT = 48cm.
SHow that ∠RTP = 90°.
The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground then the actual height of the tree is ______.
Two angles are said to be ______, if they have equal measures.
Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures 60 metres × 80 metres. How much shorter is the route across the park than the route around its edges?
