MCQOPTIONS
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MCQOPTIONS
This section includes 29 Mcqs, each offering curated multiple-choice questions to sharpen your GEOMETRY knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
A regular hexagon is inscribed in a circle of radius 5 cm. If x is the area inside the circle but outside the regular hexagon, then which one of the following is correct? |
| A. | 13 cm2<x< 15 cm2 |
| B. | 15 cm2<x< 17 cm2 |
| C. | 17 cm2<x< 19 cm2 |
| D. | 19 cm2<x< 21 cm2 |
| Answer» B. 15 cm2<x< 17 cm2 | |
| 2. |
Consider the following statements: I. The tangent of a circle is a line that meets the circle in one and only one point. II. The tangent of a circle at the end point of the diameter is perpendicular to the diameter. Which of the above statements is/are correct? |
| A. | Only I |
| B. | Only II |
| C. | Both I and II |
| D. | Neither I nor II |
| Answer» D. Neither I nor II | |
| 3. |
In a ΔABC, AB = BC = CA. The ratio of the radius of the circumcircle to that of the incircle is |
| A. | 2 : 1 |
| B. | 3 : 1 |
| C. | 3 : 2 |
| D. | None of these |
| Answer» B. 3 : 1 | |
| 4. |
The diameter of a circle with centre at C is 50 cm. CP is a radial segment of the circle. AB is a chord perpendicular to CP and passes through P. CP produced intersects the circle at D. If DP = 18 cm, then what is the length of AB? |
| A. | 24 cm |
| B. | 32 cm |
| C. | 40 cm |
| D. | 48 cm |
| Answer» E. | |
| 5. |
AB and CD are two parallel chords on the opposite sides of the centre of the circle. If AB = 10 cm, CD = 24 cm and the radius of the circle is 13 cm, the distance between the chords is |
| A. | 17 cm |
| B. | 15 cm |
| C. | 16 cm |
| D. | 18 cm |
| Answer» B. 15 cm | |
| 6. |
A circle (with centre at O) is touching two intersecting lines AX and BY. The two points of contact A and B subtend an angle of 65° at any point C on the circumference of the circle. If P is the point of intersection of the two lines, then the measure of ∠APO is |
| A. | 25° |
| B. | 65° |
| C. | 90° |
| D. | 40° |
| Answer» B. 65° | |
| 7. |
The largest chord of a circle is known to be 10.1 cm. The radius of this circle must be : |
| A. | 5 cm |
| B. | greater than 5 cm |
| C. | greater than or equal to 5 cm |
| D. | less than 5 cm |
| Answer» C. greater than or equal to 5 cm | |
| 8. |
A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°, ∠BAC is |
| A. | 120° |
| B. | 90° |
| C. | 100° |
| D. | 110° |
| Answer» E. | |
| 9. |
A, B and C are the three points on a circle such that the angles subtended by the chords AB and AC at the centre O are 90° and 110° respectively. ∠BAC is equal to |
| A. | 70° |
| B. | 80° |
| C. | 90° |
| D. | 100° |
| Answer» C. 90° | |
| 10. |
Three circles of diameter 10 cm each, are bound together by a rubber band, as shown in the figure. The length of the rubber band, in cm, if it is stretched as shown, is |
| A. | 30 |
| B. | 30 + 10π |
| C. | 10π |
| D. | 60 + 20π |
| Answer» C. 10π | |
| 11. |
The distance between two parallel chords of length 6 cm each in a circle of diametre 10 cm is |
| A. | 8 cm |
| B. | 7 cm |
| C. | 6 cm |
| D. | 5.5 cm |
| Answer» B. 7 cm | |
| 12. |
If a circle is provided with measure of 19° on centre, is it possible to divide the circle into 360 equal parts? |
| A. | Never |
| B. | Possible when one more measure of 20 is given |
| C. | Always |
| D. | Possible if one more measure of 21 is given |
| Answer» D. Possible if one more measure of 21 is given | |
| 13. |
In the given figure, O is the centre of the circle. If ∠PRQ = 40°, then what is ∠OPQ? |
| A. | 30° |
| B. | 40° |
| C. | 150° |
| D. | 50° |
| Answer» E. | |
| 14. |
A tangent YZ is drawn at any point Y of a circle of radius 3.5 cm. YX1 and YX2 are the two chords of this circle. If ∠ZYX2 = 45° and O is the centre of the circle, then the length of arc YX2 is (assume π = 22/7 ) |
| A. | 6.5 cm |
| B. | 7 cm |
| C. | 6 cm |
| D. | 5.5 cm |
| Answer» E. | |
| 15. |
In the given figure ‘O’ is the centre of the circle and PAT is the tangent at point A. Find the measures of x°, y°, and z° respectively. |
| A. | 66°, 66°, 66° |
| B. | 66°, 24°, 72° |
| C. | 24°, 24°, 96° |
| D. | 24°, 48°, 66° |
| Answer» E. | |
| 16. |
What is the area (in cm2) of shaded portion bounded by three semicircle as shown in the figure? (It is given that the radius of two smaller semicircle is 1 cm) |
| A. | 4π |
| B. | 8π – 1 /2 |
| C. | 4π – 1/2 |
| D. | None of these |
| Answer» E. | |
| 17. |
O is the centre of the circle. if ∠BAC = 52°, then ∠OCD is equal to |
| A. | 52° |
| B. | 104° |
| C. | 128° |
| D. | 76° |
| Answer» B. 104° | |
| 18. |
In a circle with centre O, AB and CD are two diameters perpendicular to each other. The length of chord AC is : |
| A. | 2 AB |
| B. | √2AB |
| C. | 1/2AB |
| D. | 1 / √2AB |
| Answer» E. | |
| 19. |
Two circles touch each other externally at P. AB is a direct common tangent to the two circles, A and B are points of contact and ∠PAB = 35° . Then ∠ABP is |
| A. | 35° |
| B. | 55° |
| C. | 75° |
| D. | 65° |
| Answer» C. 75° | |
| 20. |
Two circles touch externally at P, QR is a common tangent of the circles touching the circles at Q and R. Then measure of ∠QPR is |
| A. | 60° |
| B. | 30° |
| C. | 90° |
| D. | 45° |
| Answer» D. 45° | |
| 21. |
Two chords of lengths a metre and b metre subtend angles 60° and 90° at the centre of the circle respectively. Which of the following is true ? |
| A. | b = √2a |
| B. | a =√2b |
| C. | a = 2b |
| D. | b = 2a |
| Answer» B. a =√2b | |
| 22. |
In the given figure, ∠ONY = 50° and ∠OMY = 15°. Then the value of the ∠MON is |
| A. | 30° |
| B. | 40° |
| C. | 20° |
| D. | 70° |
| Answer» E. | |
| 23. |
A, B, C are three points on the circumference of a circle and if AB = AC = 5 √2 cm and ∠BAC = 90°, find the radius. |
| A. | 10 cm |
| B. | 5 cm |
| C. | 20 cm |
| D. | 15 cm |
| Answer» C. 20 cm | |
| 24. |
In ΔABC, ∠ABC = 70°, ∠BCA = 40°. O is the point of intersection of the perpendicular bisectors of the sides, then the angle ∠BOC is |
| A. | 100° |
| B. | 120° |
| C. | 130° |
| D. | 140° |
| Answer» E. | |
| 25. |
AB is the diameter of a circle with centre O and radius OD is perpendicular to AB. Find the angle BAD |
| A. | 60° |
| B. | 45° |
| C. | 30° |
| D. | 75° |
| Answer» C. 30° | |
| 26. |
In a right angled triangle, the circumcentre of the triangle lies. |
| A. | inside the triangle |
| B. | outside the triangle |
| C. | on the midpoint of hypotenous |
| D. | on one vertex |
| Answer» D. on one vertex | |
| 27. |
In the given figure below, ∠AOB = 48° and AC and OB intersect each other at right angles. What is the measure of ∠OBC? (O is the centre of the circle) |
| A. | 44° |
| B. | 66° |
| C. | 67° |
| D. | 78.5° |
| Answer» C. 67° | |
| 28. |
O and O' are repectively the orthocentre and cicumcentre of an acute angled triangle PQR. the point P and O are joined and produced to meet the side QR at S. If ∠PQS = 60° and ∠QO'R = 130° then ∠RPS = ? |
| A. | 45° |
| B. | 35° |
| C. | 60° |
| D. | 75° |
| Answer» C. 60° | |
| 29. |
PQ is a chord of a circle with centre O and SOR is a line segment originating from a point S on the circle and intersecting PQ produced at R such that QR = OS. If ∠QRO = 30° then ∠POS = ? |
| A. | 40° |
| B. | 70° |
| C. | 90° |
| D. | 60° |
| Answer» D. 60° | |