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Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar(△AOD) = ar(△BOC) . Prove that ABCD is a trapezium.

Solution Given: ar(ΔAOD) = ar(ΔBOC) Prove: ABCD is a trapezium. Proof: ar(ΔAOD) = ar(ΔBOC) => ar(ΔAOD) + ar(ΔAOB) = ar(ΔBOC)+ar(ΔAOB)... View Article

Solution In ΔABC, AO is the median. (CD is bisected by AB at O) Hence, ar(AOC) = ar(AOD) —————(1) also,... View Article

Given that Initial velocity u = 0 Tower height = total distance = 19.6m g = 9.8 m/s2 Find out Final... View Article

In these two circles, there is no point in common. Here, only one point “P” is common. Even here, P... View Article

Given that A die is thrown once Find out The probability of getting (i) a prime number; (ii) a number... View Article

Solution ABCD is a trapezium with,AB || DC, XY || AC Construction Join CX To Prove: ar(ADX) = ar(ACY) Proof:... View Article

The correct answer is (D). The sides of two similar triangles are in the ratio 4: 9. Let us assume... View Article

Given A ladder 10 m long reaches a window 8 m above the ground. Find out The distance of the... View Article

Given that ABC and DBC are two triangles on the same base BC. AD intersects BC at O. To Prove... View Article

Let the sides of the two squares be x m and y m. Therefore, their perimeter will be 4x and 4y respectively And area of the... View Article

OB⊥ AB then ∆OAB is a right-angled triangle OA2 = AB2 + OB2 (Pythagoras Theorem) 52 = 42 + OB2 OB2 = 52 – 42 OB2 =... View Article

Given Radius of cone (r) =5 cm Height of cone (h) = 12 cm Volume of cone = (1/3) ×... View Article

Solution Given AB = AC and AD = AB To Prove BCD is a right angle Proof In ∆ABC, AB=AC... View Article

Solution Given XY || BC, BE || AC and CF || AB To Prove ar(ΔABE) = ar(ΔAC) Proof: BCYE is... View Article

Option (B) 70° In the quadrilateral OPTQ, ∠P = 90°, ∠Q = 90° (Theorem 10.1) ∠O = 110° The sum... View Article

Solution (i) ΔACB and ΔACF lie on the same base AC and between the same parallels AC and BF. Hence, ar(ΔACB)... View Article

Solution To prove: A circle drawn with Q as centre, will pass through A, B and O (i.e. QA = QB... View Article

Let us assume that the original edge of the cube is x cm. If the edge of the cube is doubled, then... View Article

Solution Angles in the same segment are equal. So, ∠ CBD = ∠ CAD ∴ ∠ CAD = 70° ∠... View Article

As the tangents from the point are equal AP = AS OA = OA (It is the common side) OP... View Article