Quant Boosters  Geometry  Raman Sharma  Set 2

Hint: Use Appollonius Theorem
PQ^2 + PR^2 = 2 * (x^2+279)
=>2 x^2 = 576 + 144  558
=>x = 9
QR = 2x = 18

Q18) A, B and C are the vertices of a triangle of area 60 cm^2. Let AD be the median drawn from vertex A to side BC and BY be the median from vertex B to AD. If BY is extended to meet AC at E, what is the area of triangle AYE?
[OA : 5 cm^2]

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

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]


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]