Quant Boosters - Geometry - Raman Sharma - Set 2
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Q19) A circle is drawn such that its diameter coincides with the median BD of an equilateral triangle ABC of side length (4/ rt3) cm as shown in the picture. Find the area of the triangle ABC outside the circle.
OA : (π√3 - 2π)/6
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Q20) The semi perimeter of a right angled triangle is 126cm and shortest median is 53cm.what is the area of the triangle which has the largest median as its longest side?
[OA : 1260 cm^2]
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Q21) In a triangle ABC, median AM is drawn such that it divides ∠BAC in the ratio 1:2. AM is extended to D such that ∠ABD = 90. Given AC = 12 cm Find AD.
[OA: 24 cm]
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Q22) In Triangle ABC Median from A is perpendicular to Median from B. If AC = 6 and BC = 7, then what is AB?
[OA: root(17)]
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Method 1:
Method 2:
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Q23) In Triangle ABC, AB = 16 and medians AD and BE are 12 and 18 respectively. Find the area of triangle ABC
[OA: 18 root(55) ]
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Q24) XYZ is a right angled triangle, right angled at Z. If the lengths of two of the three medians of the triangle are 4√13 units and 10 units, what is the maximum possible area (in sq.units) of the triangle XYZ?
a) 48
b) 72
c) 96
d) 108[OA: 96]
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Q25) In an isosceles right angled triangle abc . Angle b is right angle . Angle bisector of anglebac is an cut at m to the median bo. Point o lies on hypotenus .om is 20 cm then the value of ab is?
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Q26) Two sides of triangle are 10cm and 5cm in length and the length of the median to the third side is 13/2 cm.The area of the triangle is 6√x cm. Then find the value of x.
[OA: 14 cm]
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Q27) A triangle has sides of length √13, √17, and 2√5. Compute the area of the triangle
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(Credits : Shubham Sharma)
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Q28) ABC is an equilateral triangle with side length 7. BP = 3 , CP = 5 . What is the length AP ?
[OA: 8]
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AC * BP + AB * CP = AP * BC
7 * 3 + 7 * 5 = 7 * AP
AP = 8
(ptlomy's theorem)
(credits : Varun Kumar Mandal)
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Q26) In a ∆ PQR, PQ=QR , angle PQR = 90° and S and T are points on PR such that PS^2 + TR^2 = ST^2 then angle SQT = ?
a. 30
b. 45
c. 60
d. 75[OA : 45]
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Q27) In a ∆ABC, ∆ = 6 , abc = 60, r = 1, then 1/a + 1/b + 1/c = ?
[OA: 47/60]
