Geometry - Online Quiz

Following quiz provides Multiple Choice Questions (MCQs) related to Geometry. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.
Q 1 - Two Lines AB and CD intersect at O.  If ∠AOC =500,Then ∠ BOD and ∠AOD  are respectively
A - 1300 ,500
B - 500, 1300
C - 600, 1200
D - 400, 1400
∠ BOD=∠ AOC (vert . opp.  ∠s) =500
∠AOC +∠AOD = 1800 ⇒ 500 +∠AOD= 1800 ⇒∠AOD=1300
∴ ∠ BOD= 500 and ∠AOD = 1300.
Q 2 - In the given figure ,what is the value  of x, if 4x= 5y
A - 1000
B - 1050
C - 1100
D - 1150
x+y = 180 ⇒ x+ 4/5 x = 180 ⇒ 5x +4x = 900 ⇒ 9x=900 ⇒ x = 100.
Q 3 - In the given figure L1 || L2 and ∠A = 650. Then ∠C= ?
A - 1100
B - 1150
C - 1200
D - 1350
∠B = ∠A = 650 (corr. ∠s).
∴ ∠B +∠C= 1800 ⇒ 650 +∠C = 1800 ⇒ ∠C = ( 1800 - 650) = 1150.
Q 4 - In the given figure , AB ll CD, ∠ABE =1200, ∠DCE = 1000 and ∠BEC =x0. Then, x= ?
A - 600
B - 500
C - 400
D - 700
Through E draw GEH ∥ AB ∥CD
AB∥ EG and BE is the transversal.
∠ ABE +∠ GEB = 1800 ⇒ 1200 +∠GEB =1800 ⇒ ∠GEB = 600
CD ∥EH and CE is the transversal. 
∴∠DCE +∠CEH = 1800  ⇒ 1000 + ∠CEH =1800  ⇒ CEH = 800
NOW ∠GEB+ ∠BEC +∠CEH = 1800 ⇒ 60+x+80 =180 ⇒ x = 40
Q 5 - In A ∆ABC ,∠A-∠B=330 and∠ B -∠C = 180  . Then∠ B =?
A - 350
B - 550
C - 450
D - 57 0
∠ A- ∠B = 330 and ∠B -∠C =180
⇒ A= 33+ B and C=B -18
= (33+B) + B + (B-18) =180
⇒ 3B =165 ⇒ B 55.
 ∴  ∠B =550.
Q 6 - Two poles of heights 6m and 11m stand vertically on a plane ground. If the distance between their  feet is 12m , what is the distance between their tops?
A - 13 m
B - 14 m
C - 15 m
D - 12.8 m
Let AB and CD be the poles such that
 AB = 6m , CD = 11 m and BD =12m 
Draw AE ⊥ CD . Then , AE = BD = 12m
CE = CD - DE = CD - AB = (11 - 6) m =5m.
from right   AEC we have
AC2 = AE2  + CE2 = (12)2 + 52 = (114 +25)=169
⇒ Ac =  √169 = 13m
∴ Distance between their tops= 13m
Q 7 - A chord of length 30cm is at a distance of 8cm from the center of a circle . The radius of the circle is
A - 11 cm
B - 13 cm
C - 15 cm
D - 17 cm
Let O be the centre of the circle and AB  be the chord. Draw OL ⊥  AB.
Then AL= 1/2 AB = (1/2 *30)cm =15 cm  and OL = 8cm.
OA2 = OL2 +AL2= 82 + (15)2  = (64  + 225 ) =289  
⇒ OA = √289  = 17cm.
∴ Radius of the circle is 17 cm.
Q 8 - In the given figure ,ABCD is a cyclic quadrilateral in which AB ||  DC and  ∠ BAD = 1000. Then , ∠ ABC=?
A - 800
B - 1000
C - 750
D - 1500
AB   DC and AD  is the transversal.
∴ ∠ADC + ∠DAB=1800 ⇒ ADC =1000 =1800 ⇒ ADC=800.
Opposite angles of a cyclic quadrilateral are supplementary.
∴ ∠ADC +∠ABC = 1800 ⇒ 800+ ∠ABC =1800 ⇒ ABC = 1000.
Q 9 - In the given fig. PAB is a secant and PT is a tangent to the circle from P. If PT = 4cm  and AB  = xcm ,  Then PB = ?
A - 2.5 cm
B - 2.6 cm
C - 2.25 cm
D - 2.75 cm
PA *PB = PT2 ⇒ 4*(4+x)=25 ⇒ 4=x = 25/4 = 6.25 ⇒ x= 2.25 cm.
Q 10 - The lengths of the diagonals of a rhombus are 24cm and 18cm respectively. The length of each side of the rhombus is
A - 12 cm
B - 9 cm
C - 15 cm
D - 8 cm
Let ABCD be a rhombus in which diagonal AC=24 cm and diagonal BD =18 cm . We know that the diagonal of a   rhombus bisect each other at right angle.
∴ OA = 1/2 AC =(1/2 *24 ) cm =12cm
OB = 1/2 BD = (1/2 *18 ) cm =9cm 
AB2 = OA2 + OB2 = (12) 2 +  92 = (144 +81) = 225 
⇒ AB = √225 = 15 cm.
∴ Each side of the rhombus is 15 cm.

    87 Lectures 
     22.5 hours 

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