Concurrent Lines and Related Theorems

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Concurrent Lines and Related Theorems: Overview

This topic covers concepts such as Centroid of a Triangle, Property of Centroid, Circumcircle, Circumradius, Position of Special Points in Equilateral Triangle, Position of Circumcentre in a Triangle, Position of Orthocentre in a Triangle, etc.

Important Questions on Concurrent Lines and Related Theorems

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For a right-angled triangle, O is the circumcentre of the triangle ABC. Now, BO=8.5 cm, find the length of BC(in cm)?

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In the figure, XY is the bisector of ZXWZXY=75°PXW is _____°

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In the figure, OB is the bisector of AOC. Find AOB(in degrees)

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The sides of a triangle is 27 cm, 36 cm and 45 cm. The inradius of the triangle is 

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The sides of the triangle are 9 cm,15 cm and 18 cm. Its area is 67.35 sq.cm.The inradius (up to 2 decimal places) of the triangle is _____cm

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The inradius of the triangle whose sides are 13 cm,14 cm and 15 cm is _____

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Find inradius (in cm) of a triangle whose sides are 32 cm,24 cm and 40 cm.

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Find inradius(in cm) of an equilateral triangle whose side is 7 cm?

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The non-concurrent lines EF,GH and KL intersect at _____.

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The lines XY and PQ are _____lines.

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Define non concurent lines with example

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For the equilateral triangle, find the position of the incentre.

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For the equilateral triangle, find the position of the circumcentre.

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In an equilateral triangle XYZ, the circumcentre, orthocentre and incentre are ______

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The radius of a circle is  16 cm. Find the radius of the pedal triangle.

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State converse of Ceva's thorem

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If D,E and F are three points on the sides of the triangle andBEEC×CFAF×ADDB=1. Then, the points D,E and F are _____

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In the triangle ABCAP,BQ and CR are concurrent at O. Then, BPPC×QCQA×ARRB=_____