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Practice Geometry Questions and Answers

O and C are the respectively orthocentre and circumcentre of ∆PQR. The line PO is extended which intersect line QR at S. such that, ∠QCR = 140°, ∠PQ...
Find the ratio between the area of the in-circle and the circum-circle of a square?
In the given Figure, Find angle BCD. If AB is a diameter & AB is parallel to CD. ...
In an obtuse angle triangle PQR, the external angle bisector of angle P intersect the extended part of line RQ at M and the external angle bisector of ...
AB and AC are two Chords of a circle with centre O. M and N are the mid points of the chords respectively. The line OM and ON are extended which intersects...
In the given figure PQRS is a square and OQR is an equilateral triangle, then find angle POS? ...
In a given Figure, ON ∥ QR and MN ∥ OR. If, PO : OQ = 2 : 3 then find MO : OQ?...
Find the distance between two parallel chords of length 24 cm each in a circle of diameter 25 cm?
A wire is moulded into a circle of radius 21 m. Then the wire is bent and shaped into a rectangle of length 36 m. Find the area of the rectangle thus forme...
PQRS is a cyclic quadrilateral of which PQ is the diameter. Diagonals PR and QS intersect at A. If SQR = 25°, then angle PAS measures
What is the ∠ SRO if O is the centre of circle, ∠ SPO = 55˚ and ∠ POR = 115 ˚ ...
A rectangle with a diagonal of length 28m is inscribed in a circle. Find the area of a circle?
If the area of ∆ ABC is 33 cm2 & G is the centroid of ∆ ABC.then the area of the ∆ BGC?
If y = 5x + c passes through point A(5, 2), what is the value of c? ...
In a circle two chords AB and CD intersect at O, if AO = 4, BO = 3 and CO is one fourth of OD then Find OD?
If the ratio of side of a ∆ is 3:4:5, and a ┴ from opposite vertex drawn to the biggest sides at D, if the length of biggest side is 10 then find ratio...
Orthocenter of an right angle triangle lies on
If median AD of an equilateral ∆ABC is 6 cm and G is centroid. Find AG?
The volume (in cu.cm.) of a right circular cylinder with radius 1 cm and height 2 cm on is: (Take π = 22/7)
If the area of ∆ ABC is 30 cm2 & G is the centroid of ∆ ABC.then the area of the ∆ AGB?
If I is the incentre of ΔABC , if ∠ BIC = 1200 , then what is the measure of ∠ BAC?
In a circle with centre O, PAX and PBY are the tangents to the circle at points A and B. from an external point P. Q is any point on the circle such that &...
In a ∆ ABC, the angle bisector of ∠A, ∠B, ∠C meet at point I, if ∠AIC is double of equilateral ∆ , then find the ∠ABC =? (in degree)...
In Fig. if QT ⊥ PR, ∠ TQR = 40 ° and ∠ SPR = 30 ° , find x and y. ...
ABC is a right angled triangle. ∠ BAC = 90o and ∠ ACB = 60o. What is the ratio of the circum radius of the triangle to the side AB? ...
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 ? ...
Triangle ABC is similar to triangle PQR and AB : PQ = 2 : 3. AD is the median to the side BC in triangle ABC and PS is the median to the side QR in triangl...
In the given figure, B and C are the centres of the two circles. ADE is the common tangent to the two circles. If the ratio of the radius of both the circl...
In the given figure, Ab = 30 cm and CD = 24 cm. What is the value (in cm) of MN? ...
AB and AC are the two tangents to a circle whose radius is 6 cm. If ∠ BAC = 60o, then what is the value (in cm) of √(AB2 + AC2)?...
In the given figure, ABC is a right angled triangle. ∠ ABC = 90 0and ∠ ACB = 60 0. If the radius of the smaller circle is 2 cm, then what is the radius...
In the given figure, O is centre of the circle. Circle has 3 tangents. If ∠ QPR = 45 0 , then what is the value (in degrees) of ∠ QOR ? ...
In the given figure, two identical circles of radius 4 cm touch each other. A and B are the centres of the two circles. If RQ is a tangent to the circle, t...
ABC is a triangle. AB = 5 cm, AC = √41 cm and BC = 8 cm. AD is perpendicular to BC. What is the area (in cm2) of triangle ABD?
In the given figure, PQR is a triangle and quadrilateral ABCD is inscribed in it. QD = 2 cm, QC = 5 cm, CR = 3 cm. BR = 4 cm. PB = 6 cm. PA = 5 cm and AD =...
In the given figure, ABCD is a square of side 14 cm. E and F are mid points of sides AB and DC respectively. EPF is a semicircle whose diameter is EF. LMNO...
In the given figure. ABCDEF is a regular hexagon whose side is 6 cm. APF, QAB, DCR and DES are equilateral triangles. What is the area (in cm2) of the shad...
Length and breadth of a rectangle are 8 cm and 6 cm respectively. The rectangle is cut on its four vertices such that the resulting figure is a regular oct...
In the given figure, radius of a circle is 14 √2 cm. PQRS is a square. EFGH, ABCD, WXYZ and LMNO are four identical squares. What is the total area (...

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