Geometry

Let O be the centre of a circle and AC be its diameter. BD is a chord intersecting AC at E. Point A is joined to B and D. If ∠BOC = 50° and ∠AOD = 110°, then ∠BEC = ?

From a point P outside a circle, PAB is a secant and PT is a tangent to the circle, where A, B and T are points on the circle. If PT = 5 cm, PA = 4 cm and AB = x cm, then x is equal to:

From a point P, which is at a distance of 10 cm from the centre O of a circle of radius 6 cm, a pair of tangents PQ and PR to the circle at points Q and R, respectively, are drawn. Then the area of the quadrilateral PQOR is equal to

Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is

In a circle, two parallel chords on the same side of the diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is

In a circle with center O and radius 1 cm, an arc AB makes a 60 degree angle at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two respective points on OA and OB, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is

Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which of the following pairs can represent (in cm) the possible length and breadth of ABCD?

Let ABC be a right-angled triangle with hypotenuse BC of length 20 cm. If AP is perpendicular to BC, then the maximum possible length of AP, in cm, is

Directions: Solve the following question and mark the best possible option. From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is

In a circle, chords PQ and TS are produced to meet at R. If RQ = 14.4 cm, PQ = 11.2 cm, and SR = 12.8 cm, then the length of chord TS is:

P is a point outside a circle with centre O, and it is 14 cm away from the centre. A secant PAB drawn from P intersects the circle at the points A and B such that PA = 10 cm and PB = 16 cm. The diameter of the circle is:

P is a point outside a circle and is 26 cm away from its centre. A secant PAB drawn intersects the circle at points A and B such that PB = 32 cm and PA = 18 cm. The radius of the circle (in cm) is: