Quant Boosters - Geometry - Raman Sharma - Set 2

• Number of Questions : 30
Topic : Geometry
Answer Key Available ? Yes
Source : Selected Questions from CAT Prep Forums.

• Q1) In the given figure, medians QX and RY of ΔPQR are perpendicular, QX = 8 and RY = 12. The area of ΔPQR is [OA: 64]

• • Q2) PQRS is a rectangle. PQ=40cm QR=30cm. Both the circles touch each other externally and also touches the two sides QS and PQ of triangle PQS. If diagonal QS is a common tangent. Find the radius of the smaller circle? [OA: 20/3]

• • Q3) In triangle ABC, angle bisectors AD and BE intersected at P. If the sides of triangle are 3, 5, 7 opposite to A, B, C respectively and BP = x and PE = y , compute for the ratio x:y where x and y are relatively prime integers.

[OA: 2 : 1]

• Credits : Sahabudeen Salaeh • Q4) A semicircle is inscribed in an equilateral triangle as shown. What fraction of the triangle lies inside the semicircle? [OA: √3π/8 ]

• Q5) In ∆ABC , AD ia the altitude from A onto the side BC. If b > c , angle C =23° and AD = abc/(b² - c²) , then angle B is equal to
a. 83°
b. 113°
c. 123°
d. 75°
e. NoT

[OA: 113]

• Q6) On a circle 26 equidistant points are marked. These points are joined to form triangles. Of the triangles formed, how many of them will have their circumcenter on one of their sides?

[OA : 312]

• Q7) ABCD is a square with side length r units .
AB is trisected by two points R and S ,
CD is trisected by two points P and Q ,
AP and DR intersect at E
AP and DS intersect at N
AQ and DR intersect at M
AQ and DS intersect at F
What is the area of the quadrilateral EMFN ?

[OA: (r/6)^2]

• Credits : Turan Bey • Q8) In the square ABCD , a line through B intersects the extension of CD at E , the side AD at F and the diagonal AC at G if BG = 9 and GF = 3 , then what is the length of EF ? [OA: 24]

• Q9) Two of the sides of a triangle are in the ratio 3:4. The medians to these sides are perpendicular to each other. If the third side of the triangle is 12root(5), find the smaller of the first two sides of the triangle.

[OA: 36]

• • Q10) The shortest median of a right-angled triangle is 25 units. If the area of the triangle is 336 sq.units, what is the length (in units) of the longest median of the triangle?

[OA: 48.5]

• • Q11) In triangle ABC, two lines DE and FG are drawn parallel to BC such that they divide AC in the ratio 2:3:5. Find the ratio of area of triangle ABC to area of the trapezium DEGF.

[OA: 100 : 21]

• Q12) The parallel sides of Trapezium is 6 and 8 units respectively. Find the length of the line segment parallel to these sides and which divides the area of trapezium in equal halves.
A. 4 √3
B. 5 √ 2
C. 7
D. 7/√2

[OA: Option b]

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