# Quant Boosters - Geometry - Raman Sharma - Set 2

• • 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

• pqx^2 - r^2x + pq = 0
tanA + tanB = r^2/pq
tanA * tanB = 1
tan(A + B) = tan 90
so A + B = 90, so C = 90
So right angle

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