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# Notes | EduRev

## JEE : Notes | EduRev

The document Notes | EduRev is a part of the JEE Course JEE Main Mock Test Series 2020 & Previous Year Papers.
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• In the triangle ABC, if â€˜Râ€™ is the circum radius then, R = a/2 sin A = b/2 sin B = c/2 sin C = abc/4Î”.
• In case of an in-circle of triangle ABC, if â€˜râ€™ is the radius of the in-circle, then r = Î”/s
= (s â€“ a) tan A/2
= (s â€“ b) tan B/2
= (s â€“ c) tan C/2
= [a sin (B/2) sin (C/2)]/ cos A/2
= [b sin (A/2) sin (C/2)]/ cos B/2
= [c sin (B/2) sin (A/2)]/ cos C/2
= 4R sin A/2 sin B/2 sin C/2
• The relation between the radius of in circle and circum circle is given by the inequality 2r â‰¤ R.
• The above inequality reduces into equality only in case of an equilateral triangle.
• If r1, r2 and r3 are the radii of the escribed circles opposite to the angles A, B and C then,
1. r= Î”/s-a, r2 = Î”/s-b, r3 = Î”/s-c
2. r1 = s tan A/2, r2 = s tan B/2, r3 = s tan C/2
3. r1 = [a cos (B/2) cos (C/2)]/ cos A/2
4. r= [b cos (C/2) cos (A/2)]/ cos B/2
5. r3 = [c cos (A/2) cos (B/2)]/ cos C/2
• Circum-center of the pedal triangle of a given triangle bisects the line joining the circum-center of the triangle to the orthocenter.
• Orthocenter of a triangle is the same as the in-centre of the pedal triangle in the same triangle.
• If I1, I2 and I3 are the centers of the escribed circles which are opposite to A, B and C respectively and I is the center of the in-circle, then triangle ABC is the pedal triangle of the triangle I1I2I3 and I is the orthocenter of the triangle I1I2I3.
• The centroid of the triangle lies on the line joining the circum center to the orthocenter and divides it in the ratio 1: 2.
• If â€˜Oâ€™ is the orthocenter and DEF is the pedal triangle of Î”ABC, where AD, BE and CF are the perpendiculars drawn from A, B and C to the opposite sides, then
1. OA = 2R cos A
2. OB = 2R cos B
3. OC = 2R cos C
4. The circum radius of the pedal triangle = R/2
5. The area of the pedal triangle is = 2Î” cos A cos B cos C
• Some Important Results:
1. tan A/2 tan B/2 = (s-c)/s
2. tan A/2 + tan B/2 = c/s cot C/2 = c(s-c)/Î”
3. tan A/2 - tan B/2 = (a-b)(s-c)/Î”
4. cot A/2 + cot B/2 = (tan A/2 + tan B/2)/ (tan A/2.tan B/2)
= c/(s-c) cot C/2
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## JEE Main Mock Test Series 2020 & Previous Year Papers

3 videos|174 docs|149 tests

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