If the orthocenter and the centroid of a triangle are the same, then the triangle is:

In ∆ABC, ∠C=90⁰, Point P and Q are on the sides AC and BC, respectively, such that  AP:PC=BQ:QC=1:2.Then,  is equal to:

In △ABC, D and E are points on the sides AB and AC, respectively, such that DE || BC and DE: BC=6:7. (Area of △ ADE): (Area of trapezium BCED) = ?

ABC is a triangle in which DE || BC and AD: DB = 5: 4. Then DE: BC is

A chord of length 16 cm is drawn in a circle of radius 10 cm. The distance of the chord from the centre of the circle is

AB and CD are two parallel chords of a circle lying on the opposite side of the centre and the distance between them is 17cm. The length of AB and CD are 10 cm and 24 cm, respectively. The radius (in cm) of the circle is

If C₁, C₂ be the centres of rwo circles and r₁, r₂ be the respective radii such that the distance between the centres is equal to the sum of the radii of the two circles, find the number of common tangents.

In ∆PQR, O is the incentre and ∠P = 42°. Then what is the measure of ∠QOR?