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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 - In the given figure, straight line AB and CD intersect at O. IF ∠δ =3∠v, then ∠v = ?
Answer : B
Explanation
COD is a straight line ∴ ∠δ + ∠v =180⁰ ⇒ 3v +v =180 ⇒ 4v = 180 ⇒ v =45⁰.
Answer : A
Explanation
The shortest distance between two intersecting lines is 0.
Q 3 - In the given figure , AB || CD, ∠BAE =110⁰ , ∠ECD = 120⁰ and ∠AEC =x⁰. Then, x= ?
Answer : A
Explanation
Draw FEG∥ AB ∥CD. AB∥ EG and AE is the transversal. ∴ ∠BAE +∠AEG = 180⁰ ⇒ 110⁰ + ∠AEG =180⁰ ⇒ ∠AEG =70⁰ Again, EG∥ CD and EC is transcersal. ∴ ∠GEC + ∠ ECD = 180⁰ ⇒ ∠GEC +120⁰ =180⁰ ⇒ ∠GEC= 60⁰ ∴ X= 70+60 =130
Answer : A
Explanation
(∠A+∠B) +(∠B+∠C) =(65⁰+140⁰)= 205⁰ ⇒ (∠A+∠B+∠C) +∠B =205⁰ ⇒ 180⁰ +∠B=205⁰ ⇒ ∠B =(205-180)⁰ =25⁰
Answer : B
Explanation
∠ 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?
Answer : A
Explanation
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
Answer : A
Explanation
Let O be the centre of the circle and AB be the chord. Draw OL ⊥ AB. Then AL= 1/2 *AB = (1/2 *16)cm =8cm and OA = 10cm. OL2 = OA2 - AL2 = (10)2 - 82 = (100 -64 ) = 36. ⇒ OL = √36 = 6cm Required distance = 6 cm
Answer : C
Explanation
Opposite angles of a cyclic quadrilateral are supplementary. ∴ ∠A + ∠C = 180 ⁰⇒ 80⁰ + C =180⁰ ⇒ C = 100⁰.
Q 9 - In the given figure, chords AB and CD of a circle intersect externally at P. If AB =6cm, CD = 3cm and PD= 5cm then PB= ?
Answer : D
Explanation
PA * PB + PC *PD ⇒ (x+6 ) * x=8* 5 ⇒ x2 +6x - 40 =0 ⇒ (x+10) (x-4) =0 ⇒ x=4 ∴ PB= 4 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
Answer : C
Explanation
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.
