Two poles of heights 6 m and 11 m stand on a plane ground. If t
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    Triangles

    Multiple Choice QuestionsLong Answer Type

    221. In the given Fig, O is a point in the interior of a triangle ABC, OD ⊥ BC,OE ⊥ AC and OF ⊥ AB. Show that
    (i) OA2 + OB2 + OC2 - OD2 - OE2 - OF2 = AF2 + BD2 + CE2,
    (ii) AF2 + BD2 + CE2 = AE2 + CD2 + BF2.
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    Multiple Choice QuestionsShort Answer Type

    222.

    A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.

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    Answer

    Multiple Choice QuestionsLong Answer Type

    224. An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1 1 half hours ?
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    225.

    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.

    Given: AD and BE are two poles of height 6 cm and 11 m respectively. D and E are their tops respectively. A and B are their feet respectively such that AB = 12 m.
    Given: AD and BE are two poles of height 6 cm and 11 m respectively.

    Required : To find out DE.
    Construction: Draw DC ⊥ BE. Join DE.
    Determination: ABCD is a rectangle and BC and AD are its opposite sides.
    ∴    BC = AD
    [∵ Opposite sides of a rectangle are equal]   = 6 m
    Similarly,    DC = AB = 12 cm
    Now,    CE = BE - BC
    = 11 m - 6 m = 5 m
    Again, in right triangle DCE,
    DE2 = DC2 + CE2
    [By Pythagoras theorem]
    = (12)2 + (5)2
    = 144 + 25 = 169
    rightwards double arrow space space space space space space space space space space space space space space DE equals square root of 169 space equals space 13 space cm
    Hence, the distance between their tops is 13 m.
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    Multiple Choice QuestionsShort Answer Type

    226. D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2 + BD2 = AB2 + DE2.
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    Multiple Choice QuestionsLong Answer Type

    227. The perpendicular from A on side BC of a ∆ABC intersects BC at D such that DB = 3 CD. Prove that 2AB2 = 2AC2 +BC2.
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    229. In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.
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    Multiple Choice QuestionsShort Answer Type

    230. Tick the correct answer and justify: In ∆ABC, AB equals 6 square root of 3 space cm comma space AC space equals space 12 space cm space and space BC space equals space 6 space cm. The angle B is:
    (A) 120°                (B) 60°
    (C) 90°                  (D) 45°
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