Mathematics

Geometry MCQs

Practice Geometry MCQs for competitive exams.

Geometry MCQs

Practice questions from this topic.

In ΔABC, D is the median from A to BC. AB = 6 cm, AC = 8 cm, and BC = 10 cm. The length of median AD (in cm) is:

A. 4.5
B. 5
C. 4
D. 3

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O is a point in the interior of ΔABC such that OA = 12 cm, OC = 9 cm, ∠AOB = ∠BOC = ∠COA and ∠ABC = 60°. What is the length (in cm) of OB?

A. 6√3
B. 4√6
C. 6√2
D. 4√3

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ln ΔABC, BD ⊥ AC at D. $$x$$ is a point on BC such that ∠BEA = $$x$$°. If ΔEAC = 62° and ΔEBD = 60°, then the value of $$x$$ is:

A. 78°
B. 68°
C. 76°
D. 92°

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PA and PB are tangents to the circle and O is the centre of the circle. The radius is 5 cm and PO is 13 cm. If the area of the triangle PAB is M, value of $$sqrt {frac{{text{M}}}{{15}}} $$ is :

A. $$sqrt {frac{{24}}{{13}}} $$
B. $$frac{{24}}{{13}}$$
C. $$frac{{12}}{{13}}$$
D. $$sqrt {frac{{12}}{{13}}} $$

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In a triangle ABC, AB = AC and the perimeter of ΔABC is 8(2 + √2) cm. If the length of BC is √2 times the length of AB, then find the area of ΔABC.

A. 32 cm 2
B. 28 cm 2
C. 16 cm 2
D. 36 cm 2

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In ΔPQR, ∠P = 90°. S and T are the mid points of sides PR and PQ, respectively. What is the value of $$frac{{{text{R}}{{text{Q}}^2}}}{{{text{Q}}{{text{S}}^2} + {text{R}}{{text{T}}^2}}} = ?$$

A. $$frac{3}{4}$$
B. $$frac{4}{5}$$
C. $$frac{1}{2}$$
D. $$frac{2}{3}$$

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In ΔPQR, ∠Q = 84° and ∠R = 48°, PS ⊥ QR at S and the bisector of ∠P meets QR at T. What is the measure of ∠SPT ?

A. 12°
B. 24°
C. 21°
D. 18°

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Two circles with centres A and B of radii 5 cm and 3 cm respectively touch each other internally. If the perpendicular bisector of AB meets the bigger circle at P and Q, then the value of PQ is

A. √6 cm
B. 2√6 cm
C. 3√6 cm
D. 4√6 cm

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In ΔABC, D and E are the midpoints of sides BC and AC, respectively, AD and BE intersect at G at right angle. If AD = 18 cm and BE = 12 cm, then the length of DC (in cm) is:

A. 10
B. 6
C. 9
D. 8

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In an equilateral ΔABC, the medians AD, BE and CF intersect to each other at point G. If the area of quadrilateral BDGF is 12√3 cm 2 , then the side of ΔABC is:

A. 10√3 cm
B. 10 cm
C. 12√3 cm
D. 12 cm

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AC is the diameter of a circle dividing the circle into two semicircles. ED is a chord in one semicircle, such that ED is parallel to AC. B is a point on the circumference of the circle in the other semicircle. ∠CBE = 75°. What is the measure (in degree) of ∠CED?

A. 68°
B. 37°
C. 75°
D. 15°

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In the following figure, P and Q are centres of two circles. The circles are intersecting at points A and B. PA produced on both the sides meets the circles at C and D. If ∠CPB = 100°, then find the value of x.

A. 115
B. 120
C. 110
D. 100

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Geometry MCQs

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Geometry MCQs

In ΔABC, D is the median from A to BC. AB = 6 cm, AC = 8 cm, and BC = 10 cm. The length of median AD (in cm) is:

O is a point in the interior of ΔABC such that OA = 12 cm, OC = 9 cm, ∠AOB = ∠BOC = ∠COA and ∠ABC = 60°. What is the length (in cm) of OB?

ln ΔABC, BD ⊥ AC at D. $$x$$ is a point on BC such that ∠BEA = $$x$$°. If ΔEAC = 62° and ΔEBD = 60°, then the value of $$x$$ is:

PA and PB are tangents to the circle and O is the centre of the circle. The radius is 5 cm and PO is 13 cm. If the area of the triangle PAB is M, value of $$sqrt {frac{{text{M}}}{{15}}} $$ is :

In a triangle ABC, AB = AC and the perimeter of ΔABC is 8(2 + √2) cm. If the length of BC is √2 times the length of AB, then find the area of ΔABC.

In ΔPQR, ∠P = 90°. S and T are the mid points of sides PR and PQ, respectively. What is the value of $$frac{{{text{R}}{{text{Q}}^2}}}{{{text{Q}}{{text{S}}^2} + {text{R}}{{text{T}}^2}}} = ?$$

In ΔPQR, ∠Q = 84° and ∠R = 48°, PS ⊥ QR at S and the bisector of ∠P meets QR at T. What is the measure of ∠SPT ?

Two circles with centres A and B of radii 5 cm and 3 cm respectively touch each other internally. If the perpendicular bisector of AB meets the bigger circle at P and Q, then the value of PQ is

In ΔABC, D and E are the midpoints of sides BC and AC, respectively, AD and BE intersect at G at right angle. If AD = 18 cm and BE = 12 cm, then the length of DC (in cm) is:

In an equilateral ΔABC, the medians AD, BE and CF intersect to each other at point G. If the area of quadrilateral BDGF is 12√3 cm 2 , then the side of ΔABC is:

AC is the diameter of a circle dividing the circle into two semicircles. ED is a chord in one semicircle, such that ED is parallel to AC. B is a point on the circumference of the circle in the other semicircle. ∠CBE = 75°. What is the measure (in degree) of ∠CED?

In the following figure, P and Q are centres of two circles. The circles are intersecting at points A and B. PA produced on both the sides meets the circles at C and D. If ∠CPB = 100°, then find the value of x.