MCQ Questions

Question No. 1

Calculate length BC in △ABC.

Answer :

Question No. 2

In △DGF, GE ⟂ DF and DG ⟂ FG. Calculate the following lengths.

Answer :

a) DG

b) EF

Question No. 3

In circle centre O, OM ⟂ AB and M is the midpoint of AB. Calculate OM if OA = 5 cm and AB = 8 cm.

Answer :

Question No. 4

DOE is a diameter of circle centre O. OM ⟂ DF and M is the midpoint of DF. OM = 7 cm and DF = 48 cm. Calculate the length of diameter DE.

Answer :

Question No. 5

△MNP is inside circle centre O. MN = 48 mm and PN = 14 mm. Calculate the length of the radius of the circle.

Answer :

Question No. 6

AB is a diameter of circle centre O. OC ⟂ chord DB and C is the midpoint of DB. If AD = 4√3 cm and DB = 4 cm, calculate:

Answer :

a) OC

b) AB

Question No. 7

△ABC is in circle centre O with AB the diameter and OM ⟂ AC and BC ⟂ AC. AO = 10 mm, AM = 6 mm and BC = 16 mm. Calculate:

Answer :

a) OM

b) AC

Question No. 8

In circle centre O, ON ⟂ PQ.

Answer :

a) Prove that NQ² = 2·ON·MN.

b) If the radius = 9 cm and OM = 1 cm, calculate NQ.

Question No. 9

Given: circle with centre M and chord PR with midpoint Q.

Answer :

a) If radius MP = 5 cm and PR = 8 cm, calculate length MQ.

b) If MQ = 8 cm and QR = 15 cm, calculate the length of the radius.

c) If radius MR = 13 cm and MQ = 5 cm, calculate length PR.

Question No. 10

M is the midpoint of chord AB in circle centre O. AB = 10 cm and the radius = 13 cm. Calculate the length of MP.

Answer :

Question No. 11

In the circle, O is the centre and R is the midpoint of chord PQ. If PQ = 12 cm and RS = 2 cm, calculate:

Answer :

a) x

b) r

Question No. 12

In circle centre O, M and N are midpoints of chords AB and CD respectively. CD = 48 mm, ON = 7 mm and OM = 5 mm. Calculate the length AB (to the nearest cm).

Answer :

Question No. 13

C is the midpoint of chord AB in the circle with centre O. OC = 40 cm and AB = 80 cm. Calculate the length of the diameter (leave answer in simplified surd form).

Answer :

Question No. 14

AB is a chord of circle with centre O. OP ⊥ AB and cuts AB at Q and the circle at P. If the radius is 13 cm and AQ = 12 cm, calculate:

Answer :

a) AB

b) AP (leave the answer in surd form)

Question No. 15

OT = MT = TN in circle centre O. Calculate the size of ∠N.

Answer :

Question No. 16

In circle centre M, CD ⊥ AB. If AB = 30 cm and CE = 5 ED, calculate:

Answer :

a) DE

b) diameter of the circle

Question No. 17

In circle centre O, line OCD ⊥ AB and cuts AB at C. If chord AB = 6 cm and CD = 1 cm, find the length OC.

Answer :

Question No. 18

ABC is a double chord in the circles with centres O and P. OP ∥ ABC, OM ⊥ AB and PN ⊥ BC. Prove that:

Answer :

a) OPNM is a rectangle

b) OP = ½ AC

Question No. 19

Two concentric circles have radii 17 cm and 25 cm. OC = 15 cm and OC ⟂ ABDE. Calculate the length AB.

Answer :

Question No. 20

Chord AB = 80 cm and chord CD = 60 cm. OE ⟂ AB and OF ⟂ CD. The radius of the circle is 50 cm. Find the distance between the two chords.

Answer :

Question No. 21

The two concentric circles with centre O have radii 5 cm and 8.5 cm. BC = 6 cm and OM ⟂ ABCD. Calculate the length AD.

Answer :

Question No. 22

Chord AB = 30 cm and chord CD = 40 cm and AB  CD. OM ⟂ AB and ON ⟂ CD. If the radius of the circle is 25 cm, calculate the distance between the chords.

Answer :

Question No. 23

ABC is a double chord of the circles with centres M and P. The circles intersect at B and D. Prove that AC = 2MP.

Answer :

Question No. 24

MN and PQ are parallel chords in the circle with centre O. MN = 80 cm and PQ = 52 cm. The radius of the circle = 60 cm. ORS is perpendicular to chords MN and PQ. Calculate the distance between the chords. Write the answer correct to two decimal places.

Answer :

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