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
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?
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
Raman_Sharma last edited by Raman_Sharma
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 ?
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 ?
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.
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?
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
[OA: Option b]