Aptitude · all questions

Geometry
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Q161

Let D and E be two points on the side BC of ΔABC such that AD = AE and ∠BAD = ∠EAC. If AB = (3x + 1) cm, BD = 9 cm, AC = 34 cm and EC = (y + 1) cm, then the value of (x + y) is:

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Q162

In the given figure, PQRS is a square inscribed in a circle of radius 4 cm. PQ is produced till point Y. From Y a tangent is drawn to the circle at point R. What is the length (in cm) of SY?
Geometry mcq question image

Geometry mcq question image

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Q163

ABC is an isosceles triangle where AB = AC which is circumscribed about a circle. If P is the point where the circle touches the side BC, then which of the following is true?

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Q164

AB is a diameter of a circle with centre O, CB is a tangent to the circle at B. AC intersects the circle at G. If the radius of the circle is 6 cm and AG = 8 cm, then the length of BC is:

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Q165

A circle is inscribed in a triangle ABC. It touches side AB, BC and AC at points R, P and Q, respectively. If AQ = 2.6 cm, PC = 2.7 cm and BR = 3 cm, then the perimeter (in cm) of the triangle ΔABC is:

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Q166

PQR is a triangle. S and T are the midpoints of the sides PQ and PR respectively. which of the following is TRUE?
I. Triangle PST is similar to triangle PQR.
II. ST =

\frac{1}{2}

(QR)
III. ST is parallel to QR.

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Q167

B₁ is a point on the side AC of ΔABC and B₁B is joined. A line is drawn through A parallel to B₁B meeting BC at A₁ and another line is drawn through C parallel to B₁B meeting AB produced at C₁. Then

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Q168

In a circle with centre O, ABCD is a cyclic quadrilateral and AC is the diameter. Chords AB and DC are produced to meet at E. If ∠CAE = 34° and ∠E = 30°, then ∠CBD is equal to:

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Q169

G is the centroid of the triangle ABC. where AB, BC and CA are 7 cm, 24 cm and 25 cm respectively. than BG is:

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Q170

Two circles touch externally. The sum of their areas is 130π sq cm and the distance between their centres is 14 cm. The radius of the smaller circle is:

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Q171

A is a point at a distance 26 cm from the centre O of a circle of radius 10 cm. AP and AQ are the tangents to the circle at the point of contacts P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B, AQ at C, then the perimeter of ΔABC is:

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Q172

In a circle, PQ and RS are two diameters that are perpendicular to each other. Find the length of the chord PR.

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Q173

Let AX ⊥ BC of an equilateral triangle ABC. Then the sum of the perpendicular distances of the sides of ΔABC from any point inside the triangle is:

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Q174

In the figure below, AB is a chord of a circle with centre O. A tangent AT is drawn at point A so that ∠BAT = 50°. Then ∠ADB = ?
Geometry mcq question image

Geometry mcq question image

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Q175

Two circles with the same centre P have radii 7.5 cm and 4.4 cm. Through a point A of the larger circle, a tangent is drawn to the smaller circle touching it at B. Find AC (Approximate in cm).

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Q176

In ΔABC, E and D are points on sides AB and AC, respectively, such that ∠ABC = ∠ADE. If AE = 6 cm, AD = 4 cm and EB = 4 cm, then the length of DC is:

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Q177

A secant PAB is drawn from an external point P to the circle with centre O, intersecting it at A and B. If OP = 17 cm, PA = 12 cm and PB = 22.5 cm, then the radius of the circle is:

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Q178

In the given, figure, CD and AB are diameters of circle and AB and CD are perpendicular to each other, LQ and SR are perpendiculars to AB and CD respectively. Radius of circle is 5 cm, PB : PA = 2 : 3. What is the length (in cm) of SM?

Geometry mcq question image

Geometry mcq question image

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Q179

In the following figure (not to scale), at the centre O, if the chord AB students double the angle that is subtended by chord CD and the angle ∠AEB = 2∠AOB, then ∠COD is equal to:
Geometry mcq question image

Geometry mcq question image

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Q180

A circle inscribed in a triangle ABC touches its sides AB, BC and AC at the points D, E and F, respectively. If AB = 18 cm, BC = 15 cm and AC = 13 cm, then the value of AD + BE + CF is:

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