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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 - Two Lines AB and CD intersect at O. If ∠AOC =50⁰,Then ∠ BOD and ∠AOD are respectively
Answer : B
Explanation
∠ BOD=∠ AOC (vert . opp. ∠s) =50⁰ ∠AOC +∠AOD = 180⁰ ⇒ 50⁰ +∠AOD= 180⁰ ⇒∠AOD=130⁰ ∴ ∠ BOD= 50⁰ and ∠AOD = 130⁰.
Answer : A
Explanation
The shortest distance between two intersecting lines is 0.
Answer : B
Explanation
∠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= ?
Answer : C
Explanation
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 - The angle of a triangle are 3x⁰, (2x-7)⁰ and (4x-11)⁰. The value of x is :
Answer : A
Explanation
The sum of the angle of a triangle is 180⁰. ∴ 3x = 2x - 7 + 4x -11 = 180 ⇒ 9x =162 ⇒ x = 18. Hence, x = 18.
Q 6 - The perimeters of two similar triangles ∆ ABC and∆ PQR are 36cm and 24 cm . If PQ= 10cm, Then AB=?
Answer : C
Explanation
we have AB/PQ = 36/24 ⇒ AB / 10 = 3/2 ⇒ AB = (3/2 * 10) = 15 cm.
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 : D
Explanation
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=?
Answer : B
Explanation
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 = ?
Answer : C
Explanation
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
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.
