Quant Boosters  Geometry  Raman Sharma  Set 2

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]


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)]

Method 1:
Method 2:

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) ]


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]

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?


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]

Q27) A triangle has sides of length √13, √17, and 2√5. Compute the area of the triangle

(Credits : Shubham Sharma)

Q28) ABC is an equilateral triangle with side length 7. BP = 3 , CP = 5 . What is the length AP ?
[OA: 8]

AC * BP + AB * CP = AP * BC
7 * 3 + 7 * 5 = 7 * AP
AP = 8
(ptlomy's theorem)
(credits : Varun Kumar Mandal)

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]


Q27) In a ∆ABC, ∆ = 6 , abc = 60, r = 1, then 1/a + 1/b + 1/c = ?
[OA: 47/60]

Q28) There is a square ABCD. There is a point P inside this square such that PA = 4, PB = 1, PD = 5. Find area of the square.
[OA : 17]

(credits : Anil Sharma)

Q29) In a ∆ABC , if tanA and tanB are the roots of the of pq(x²+1) = r²x. Then ∆ABC is
a. Right angled
b. Obtuse angled
c. Equilateral
d. Acute angled