Advertisements
Advertisements
प्रश्न
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`
Advertisements
उत्तर
We have ∠AED = 90°
∴ ∠ADE < 90° and ∠ADC > 90°
i.e. ∠ADE is acute and ∠ADC is obtuse.
In ΔADC, ∠ADC is an obtuse angle.
∴ AC2 = AD2 + DC2 + 2 x DC x DE
⇒ AC2 = AD2 + `(1/2"BC")^2 + 2 xx (1)/(2)"BC" xx "DE"`
⇒ AC2 = AD2 + `(1)/(4)"BC"^2 + "BC" xx "DE"`
⇒ AC2 = AD2 + BC x DE + `(1)/(4)"BC"^2` . ....(i)
APPEARS IN
संबंधित प्रश्न
If the sides of a triangle are 6 cm, 8 cm and 10 cm, respectively, then determine whether the triangle is a right angle triangle or not.
A ladder leaning against a wall makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder
Two towers of heights 10 m and 30 m stand on a plane ground. If the distance between their feet is 15 m, find the distance between their tops
In Fig., ∆ABC is an obtuse triangle, obtuse angled at B. If AD ⊥ CB, prove that AC2 = AB2 + BC2 + 2BC × BD
The perpendicular AD on the base BC of a ∆ABC intersects BC at D so that DB = 3 CD. Prove that `2"AB"^2 = 2"AC"^2 + "BC"^2`
Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals
Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(A)\[7 + \sqrt{5}\]
(B) 5
(C) 10
(D) 12
Prove that the points A(0, −1), B(−2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD?
In the figure: ∠PSQ = 90o, PQ = 10 cm, QS = 6 cm and RQ = 9 cm. Calculate the length of PR.
Triangle ABC is right-angled at vertex A. Calculate the length of BC, if AB = 18 cm and AC = 24 cm.
In the given figure, angle BAC = 90°, AC = 400 m, and AB = 300 m. Find the length of BC.
In triangle PQR, angle Q = 90°, find: PQ, if PR = 34 cm and QR = 30 cm
In the given figure, AD = 13 cm, BC = 12 cm, AB = 3 cm and angle ACD = angle ABC = 90°. Find the length of DC.
Find the Pythagorean triplet from among the following set of numbers.
2, 4, 5
From a point O in the interior of aΔABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that: AF2 + BD2 + CE2 = OA2 + OB2 + OC2 - OD2 - OE2 - OF2
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 - AB2 = 2BC x ED
Sides AB and BE of a right triangle, right-angled at B are of lengths 16 cm and 8 cm respectively. The length of the side of largest square FDGB that can be inscribed in the triangle ABE is ______.
In a right-angled triangle ABC, if angle B = 90°, then which of the following is true?
