In the triangle PQR, AB is parallel to QR. The ratio of the areas of two similar triangles PAB and PQR id 1:2. Then PQ:AQ = __________________.
(1)
(2)
(3)
(4)
In the figure given below, equilateral triangle ECB surmounts square ABCD. Find the angle BED represented by x.
(1)
(2)
(3)
(4)
In two triangles ABC and DEF, . The sum of the angles A and B is equal to the sum of the angles D and E. If BC = 6 cm and EF = 8 cm, find the ratio of the area of the triangles, ABC and DEF.
(1) 3 : 4
(2) 4 : 3
(3) 9 : 16
(4) 16 : 9
In the following figure, PQ is parallel to BC and PQ : BC = 1 : 3. If the area of the triangle ABC is 144 , then what is the area of the triangle APQ?
(1) 48
(2) 36
(3) 16
(4) 9
In triangle ABC, sides AB and AC are extended to D and E, respectively, such that AB = BD and AC = CE. Find DE, if BC = 6 cm.
(1) 3 cm
(2) 6 cm
(3) 9 cm
(4) 12 cm
A man travels on a bicycle, 10 km east from the starting point A to reach point B, then he cycles 15 km south to reach point C. Find the shortest distance between A and C.
(1) 25 km
(2) 5 km
(3) km
(4) km
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
PT and PS are the tangents to the circle with centre O. If
(1)
(2)
(3)
(4)
In the following figure X, Y and Z are the points at which the incircle touches the sides of the triangle. If PX = 4 cm, QZ = 7 cm and YR = 9 cm, then the perimeter of triangle PQR is
(1) 20 cm
(2) 46 cm
(3) 40 cm
(4) 80 cm
The locus of the point P which is at a constant distance of 2 units from the origin and which lies in the first or the second quadrants is_______________
(1)
(2)
(3)
(4)
(1) y = 0
(2) xy = 0
(3) x = y
(4) x = 0
In the following figure, if the angle between two chords AB and AC is , then the angle between two tangents which are drawn at B and C is ________________
(1)
(2)
(3)
(4)
In the following figure, O is the centre of the circle and , find the angle between the two tangents AP and BP.
(1)
(2)
(3)
(4)
If ABCD is a square inscribed in a circle and PA is a tangent, then the angle between the lines P'A and P'B is_____________
(1)
(2)
(3)
(4)
In the following figure, if l and m are two tangents and AB is a chord making an angle of with the tangent l, then the angle between l and m is____________
(1)
(2)
(3)
(4)
Find the length of a transverse common tangent of the two circles whose radii are 3.5 cm, 4.5 cm and the distance between their centres is 10 cm.
(1) 36 cm
(2) 6 cm
(3) 64 cm
(4) 8 cm
If ABCD is a trapezium, AC and BD are the diagonals interesting each other at point O. Then AC:BD = __________
(1) AB : CD
(2) AB + AD : DC + BC
(3)
(4) AO - OC : OB - OD
In the following figure (not to scale), are equal chords and ABCD is a cyclic quadrilateral. If
(1)
(2)
(3)
(4)
In trapezium KLMN, KL and MN are parallel sides. A line is drawn, from the point A on KN, parallel to MN meeting LM at B. KN : LM is equal to ____________________
(1) KL : NM
(2) (KL + KA) : (NM + BM)
(3) (KA - AN) : (LB - BM)
(4)
In the following figure, ABCD is a square and AED is an equilateral triangle. Find the value of a.
(1)
(2)
(3)
(4)
A circle with centre O is inscribed in a quardrilateral ABCD as shown in the figure. Which of the following statements is / are true?
(A)
(B)
(C)
(1) Both (A) and (B)
(2) Both (B) and (C)
(3) Both (A) and (C)
(4) all the three
In the following figure, O is the centre of the circle and if , then the acute angle between AB and the tangent PQ at B is _______________.
(1)
(2)
(3)
(4)
In the following figure, AB = OB and CT is the tangent to the circle at O. If
(1)
(2)
(3)
(4)
AR and BS are the tangents to the circle, with centre O, touching at P and Q respectively and PQ is the chord. If
(1)
(2)
(3)
(4)
(1) scalene
(2) equilateral
(3) right angled
(4) acute angled
In the following figure, AQ is a tangent to the circle at A. If
(1)
(2)
(3)
(4)
In the following figure, two circles X and Y with centres A and B respectively interesect at C and D. The radii AC and AD of circle X are tangents to the circle Y. Radii BC and BD of circle Y are tangents to the circle X. Find
(1)
(2)
(3)
(4) Cannot be determined
The tangent AB touches a circle, with centre O, at the point P. If the radius of the circle is 5 cm, OB = 10 cm and OB = AB, then find AP.
(1)
(2)
(3)
(4)
In the following figure, O is the centre of the circle and D, E and F are mid-points of AB, BO and OA respectively. If
(1)
(2)
(3)
(4)
In the figure given below, ABC is an equilateral triangle and PQRS is a square of side 6 cm. By how many is the area of the triangle more than that of the square ?
(1)
(2) 21
(3)
(4) 63
In the following figure (not to scale) ABCD is a rectangle, BC = 24 cm, DP = 10 cm and CD = 15 cm. Then, AQ and CQ respectively are ______________.
(1) 39 cm, 13 cm
(2) 13 cm, 12 cm
(3) 25 cm, 13 cm
(4) 39 cm, 12 cm
At a particular time, the shadow cast by a tower is 6 m long. If the distance from top of the tower to the end of the shadow is 10 m long, determine the height of the tower.
(1) 4 m
(2) 8 m
(3) 16 m
(4) 12 m
(1) 74
(2) 84
(3) 91
(4) 105
(1)
(2)
(3)
(4)
In the following figure, AD
(1) 1.8 cm
(2) 2.25 cm
(3) 2.2 cm
(4) 1.85 cm
In the given figure, AB is a diameter, O is the centre of the circle and
(1)
(2)
(3)
(4)
In the following figure, O is the centre of the circle and AD is the diameter. If
(1)
(2)
(3)
(4)
In the following figure, O is the centre of the circle, AC is the diameter and if
(1)
(2)
(3)
(4)
In the trapezium PQRS, PQ is parallel to RS and the ratio of the areas of the triangle POQ to triangle ROS is 225:900. Then SR = _____________.
(1) 30 PQ
(2) 25 PQ
(3) 2 PQ
(4) PQ
In the following figure, ABCD is a parallelogram, CB is extended to F and the line joining D and F intersect AB at E. Then ____________.
(1)
(2)
(3)
(4) All of these
(1) QD:
(2)
(3)
(4) None of these
Two circles intersect at two points P and S. QR is a tangent to the two circles at Q and R. If
(1)
(2)
(3)
(4)
An equilateral triangle CDE is constructed on a side CD of square ABCD. The measure of can be ________
(1)
(2)
(3)
(4)
In the figure above (not to scale), PQ is a tangent segment to the circle at P. If p, R, S and T are concyclic points,
(1)
(2)
(3)
(4)
Construct the incircle of a given triangle ABC. The following sentences are the steps involved in the above construction. Arrange them in sequencial order from first to last.
(A) Draw perpendicular
(B) Taking I as centre and IM as the radius, draw a circle.
(C) Draw a DABC with the given measurements.
(D) Draw bisectors of two of the angles, say
(1) DCAB
(2) CDAB
(3) CADB
(4) DACB
Construct a regular pentagon in a circle of radius 4 cm. The following sentences are the steps involved in the following constructions. Arrange them in sequential order from first to last.
(A) With D as centre and AB as radius draw an arc which cuts the circle at the point C.
(B) With A as centre and AB as radius draw an arc which cuts the circle at the point E.
(C) Construct a circle with radius 4 cm.
(D) Join AB.
(E) Draw two radii
(F) Join AE, ED, DC and CB.
(G) With E as centre and AB as radius draw an arc which cuts the circle at the point D.
(1) CEDGBAF
(2) CEBDGAF
(3) CEDBGAF
(4) CEBGADF
In the diagram, O is the centre of the circle and .
(1)
(2)
(3)
(4)
Side of a square PQRS is 4 cm long.
(1)
(2)
(3) cm
(4)
ABC is an equilateral triangle of side 6 cm. If a circle of radius 1 cm is moving inside and along the sides of the triangle, then locus of the centre of the circle is an equilateral triangle of side _______________.
(1) 5 cm
(2) 4 cm
(3)
(4)
In the following figure (not to scale), STM and MQ are tangents to the circle at T and Q respectively. SRQ is a straight line. SR = TR and
(1)
(2)
(3)
(4)
PQ is the direct common tangent of two circles (S, 9 cm) and (R, 4 cm) which touch each other externally. Find the area of the quadrilateral PQRD (in ).
(1) 72
(2) 65
(3) 78
(4) 69
Diagonal AC of a rectangle ABCD is produced to the point E such that AC:CE = 2:1. AB = 8 cm and BC = 6 cm. Find the length of DE.
(1)
(2) 15 cm
(3)
(4) 13 cm
(1)
(2)
(3)
(4)
In the following figure (not to scale), ABCD is an isosceles trapezium.
(1) 11 cm
(2) 10.5 cm
(3) 10 cm
(4) 9.5 cm
P, Q and R are on AB, BC and AC of the equilateral triangle ABC respectively. AP:PB=CQ:QB=1:2. G is the centroid of the triangle PQB and R is the mid-point of AC. Find BG:GR.
(1) 1:2
(2) 2:3
(3) 3:4
(4) 4:5
In the given figure (not to scale), two circles and intersect at S and Q. PQN and RQM are tangents drawn to and respectively at Q. MAB and ABN are the chords of the circles and . If , then find .
(1)
(2)
(3)
(4) Cannot be determined
Two sides of a triangle are 5 cm and 12 cm long. The measure of third side is an integer in cm. If the triangle is an obtuse triangle, then how many such triangles are possible?
(1) 9
(2) 8
(3) 7
(4) 6
(1)
(2)
(3)
(4)
In the following figure, (not to scale), AB is the common tangent to the circles and . and are touching externally at C. AD and DC are two chords of the circle and BE and CE are two chords of the circle . Find the measure of
(1)
(2)
(3)
(4)