Aptitude · all questions

Geometry
practice.

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264

Questions

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Q121

PQR is an isosceles triangle such that PQ = QR = 10 cm and ΔPQR = 90°. What is the length of the perpendicular drawn from Q on PR?

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Q122

ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 118°. What is the measure of ∠BAC?

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Q123

In quadrilateral ABCD, the bisectors of ∠A and ∠B meet at O and ∠AOB = 64°. ∠C + ∠D is equal to:

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Q124

If the parallel sides of a trapezium are 8 cm and 4 cm, M and N are the mid points of the diagonals of the trapezium, then length of MN is.

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Q125

DE is a tangent to the circumcircle of ΔABC at the vertex A such that DE || BC. If AB = 17 cm, then the length of AC is equal to

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Q126

If D, E and F are the mid points of BC, CA and AB respectively of the ΔABC. The ratio of area of the parallelogram DEFB and area, of the trapezium CAFD is:

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Q127

At least two pairs of consecutive angles are congruent in a . . . . . . . .

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Q128

Two circles having radii

r

units intersect each other in such a way that each of them passes through the centre of the other. Then the length of their common chord is

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Q129

In the given figure, ABC is a right-angled triangle. ∠ABC = 90° and ∠ACB = 60°. If the radius of the smaller circle is 2 cm, then what is the radius (in cm) of the larger circle?
Geometry mcq question image

Geometry mcq question image

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Q130

AB and CD are two chords in a circle with centre O and AD is a diameter. AB and CD produced meet at a point P outside the circle. ∠APD = 25° and ∠DAP = 39°, then the measure of ∠CBD is:

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Q131

AD is perpendicular to the internal bisector of ∠ABC of ΔABC. DE is drawn through D and parallel to BC to meet AC at E. If the length of AC is 12 cm, then the length of AE (in cm.) is

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Q132

In the given figure, ABCD is a square whose side is 4 cm. P is a point on the side AD. What is the minimum value (in cm) of BP + CP?
Geometry mcq question image

Geometry mcq question image

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Q133

Select the correct option with respect to the given statement.
Two tangents are drawn at the end of the diameter of a circle.

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Q134

Two circles touch each other externally at T. RS is a direct common tangent to the two circles touching the circles at P and Q. ∠TPQ = 42°. ∠PQT (in degrees) is:

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Q135

In ΔABC, ∠ABC = 6∠ACB and ∠BAC = 5∠ACB. If AB = 7 cm and AC = 25 cm, then the length of BC is equal to:

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Q136

In a triangle ABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm. Then measure of ∠B is equal to:

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Q137

ABCD is a trapezium in which AB || DC and its diagonals intersect at P. If AP = (3x - 1) cm. PC = (5x - 3) cm. BP = (2x + 1) cm and PD = (6x - 5) cm, then the length of DB is:

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Q138

In ΔABC, D is a point on side BC such that ∠ADC = ∠BAC. If CA = 12 cm, CB = 8 cm, then CD is equal to:

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Q139

A circle is inscribed in a quadrilateral ABCD touching AB, BC, CD and AD at the points P, Q, R and S, respectively, and ∠B = 90°. If AD = 24 cm, AB = 27 cm and DR = 6 cm, then what is the circumference of the circle?

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Q140

In a circle, O is the centre of the circle. Chords AB and CD intersect at P. If ∠AOD = 32° and ∠COB = 26°, then the measure of ∠APD lies between:

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