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Q)Â Two circles with centres O and O’ of radii 6 cm and 8 cm, respectively intersect at two points P and Q such that OP and O’P are tangents to the two circles. Find the length of the common chord PQ. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Step 1: Since OP is O’P OO’2 […]
Two circles with centres O and O’ of radii 6 cm and 8 cm, respectively intersect at two Read More »
Q) A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 10 cm and 8 cm respectively. Find the lengths of the sides AB and AC, if it is given that area â–² ABC = 90 cm². Ans: Step 1: Let’s join
Q) One observer estimates the angle of elevation to the basket of a hot air balloon to be 60°, while another observer 100 m away estimates the angle of elevation to be 30°. Find: (a) The height of the basket from the ground. (b) The distance of the basket from the first observer’s eye. (c)
Q) Prove that: Ans: Let’s start from LHS = = = = We know that, a3−b3 formula is = (a−b)(a2 + b2 + ab) = = = = sec θ cosec θ + 1 = 1 + sec θ cosec θ = RHS Hence ProvedÂ
Prove that: tan θ /(1 – cot θ) + cot θ / (1 – tan θ) = 1 + sec θ cosecθ Read More »
Q)Â Two people are 16 km apart on a straight road. They start walking at the same time. If they walk towards each other with different speeds, they will meet in 2 hours. Had they walked in the same direction with same speeds as before, they would have met in 8 hours. Find their walking speeds.
Two people are 16 km apart on a straight road. They start Read More »
Q) In the given figure, ABCD is a parallelogram. BE bisects CD at M and intersects AC at L. Prove that EL = 2BL. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Given that: BE bisects CD at M, DM = MC Let’s look at Δ ALE and Δ CLB: ∠ALE = ∠CLB   (vertically
Q) In the given figure, CD is perpendicular bisector of AB. EF is perpendicular to CD. AE intersects CD at G. Prove that CF/CD = FG/DG. Ans: Given that: CD is perpendicular bisector of AB, AD = BD, ∠CDB = ∠GDA = 900 EF is perpendicular bisector of CD, ∠EFC = âˆ
In the given figure, CD is perpendicular bisector of AB. EF is perpendicular to CD. Read More »
Q)Â PT is the tangent to the circle centered at O. OC is Perpendicular to the chord AB. Prove that PA.PB = PC2-AC2. Ans: Let’s starts from LHS: PA . PB = (PC – AC) (PC + BC) Given that PC is to chord AB, therefore it bisects chord AB (by circle’s property) Hence, AC =
Q) If pth term of an A.P. is q and qth term is p, then prove that its nth term is (p + q – n). Ans: Step 1: We know that nth term of an A.P. is given by: Tn = a + (n -1) d Therefore, pth term, Tp = a + (p
Q)Â The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change together next? Ans: The three traffic light will change together again when the time gap is perfect multiple of each light’s interval. Therefore,