MCQ
Geometry MCQ - Practice Questions with Answers
Solve 48 Geometry questions for RAS/RPSC preparation.
Practice questions
Q1Tangents from a lamp-post to a circular flower bed are each 5 m long, and the lamp-post stands 13 m from the bed's centre. The ratio of the bed's radius to the length of each tangent equals
The radius to a point of contact is perpendicular to the tangent, so by Pythagoras r = √(13² − 5²) = √(169 − 25) = √144 = 12 m. The required ratio is therefore 12 : 5.
Q2A straight channel from a pier cuts a circular reef, meeting the near shore 4 km from the pier and the far shore 25 km from the pier. The length of a tangent from the pier to the reef is
By the tangent-secant (power of a point) theorem, (tangent)² = (external secant segment) × (whole secant). So t² = 4 × 25 = 100, hence t = 10 km.
Q3The angle that a chord subtends at the centre of a circle is 72° more than the angle it subtends at a point on the remaining circumference. The central angle is:
Let the inscribed angle be x. Then the central angle for the same arc is 2x. The problem states 2x = x + 72°, so x = 72°. Therefore the central angle is 2x = 144°.
Q4A craftsman builds two similar triangular wooden frames. The smaller has sides 9 cm, 12 cm and 15 cm, and the larger has longest side 25 cm. If the area of the smaller frame is 54 cm², the area of the larger frame is:
The longest sides correspond, so the similarity ratio of larger to smaller is 25/15 = 5/3. Areas of similar triangles scale with the square of this ratio, (5/3)² = 25/9. Therefore the larger area is 54 × (25/9) = 150 cm².
Q5A spectator on a circular gallery views a stage chord under an inscribed angle of 39°. The measure of the arc intercepted by that angle is:
The inscribed-angle theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Therefore the intercepted arc measures 2 × 39° = 78°.
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More questions
6A pair of pipe cross-sections have radii 14 cm and 8 cm, and the distance between their centres is 10 cm. The number of common tangents to both sections is:
7Two circular lids, each of radius 7 cm, rest on a bench with their centres 21 cm apart. How many common tangents can be drawn to both lids?
8Two circular lathe blanks of radii 11 cm and 4 cm have centres 25 cm apart. Find the length of a direct (external) common tangent.
9In △PQR, ∠QPR = 54°. If O denotes the circumcentre of △PQR, then ∠QOR equals:
10Measured from a vertex to the midpoint of the opposite side, the centroid of a triangular sail divides each median in the ratio:
11Workshop gauges show two pulleys of radii 10 cm and 6 cm with centres 20 cm apart. The length of a transverse (crossing) common tangent to both pulleys is:
12From a point outside a circular pulley, two tangents each 12 cm long enclose a 60° angle. The pulley's radius equals?
13In a right-angled triangular plate ABC with ∠C = 90°, the legs are AC = 9 cm and BC = 12 cm. The altitude from C meets the hypotenuse AB at D. The length of CD is:
14An equilateral triangular ceramic tile has side length 6√3 cm. Its inradius is
15On a circular warehouse dome, points W and Z lie on the same side of chord XY. If ∠XWY measures 37°, then ∠XZY equals