CBSE ICSE JEE NEET FOUNDATION CLASS 10 12

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2021-08-08 22:04:48 Karan ओपन / कमेंट

2021-07-25 09:27:06 CBSE ICSE JEE NEET FOUNDATION CLASS 10 12 pinned a photo ओपन / कमेंट

2021-07-25 09:26:17 Hi Students,

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2021-07-24 19:46:33 • NEET 2021 Free Mock Test No.4
Full Syllabus Test (180 Questions)

Date: 25-07-2021, Sunday
Duration: 180 minutes
Platform : Marvel Prep App

Batch: Marvel Free Mock Test 2021
Batch code: MPF01
Download Link for MarvelPrep App : https://tinyurl.com/ydqjabja

Note :
1. Test Opens in App from 1.45 pm (25-7-2021) to 2 pm (26-7-2021).
2. You can write at any time during this duration.
3. Once you started the test, you should complete the test within 180 minutes.
4. Also don't go out from App while attending the exam.
5. Only 2 times allowed to go out from the app.
6. If you go out from the app more than 3 times, the test will be submitted automatically showing a 0 mark.
7. Also be ensure good mobile data network ओपन / कमेंट

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2021-07-07 18:45:40 Notes on Circles Connected with Triangle

In the triangle ABC, if ‘R’ is the circum radius then, R = a/2 sin A = b/2 sin B = c/2 sin C = abc/4Δ.

In case of an in-circle of triangle ABC, if ‘r’ is the radius of the in-circle, then r = Δ/s

= (s – a) tan A/2

= (s – b) tan B/2

= (s – 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 ≤ 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,

r1 = Δ/s-a, r2 = Δ/s-b, r3 = Δ/s-c

r1 = s tan A/2, r2 = s tan B/2, r3 = s tan C/2

r1 = [a cos (B/2) cos (C/2)]/ cos A/2

r2 = [b cos (C/2) cos (A/2)]/ cos B/2

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 ‘O’ is the orthocenter and DEF is the pedal triangle of ΔABC, where AD, BE and CF are the perpendiculars drawn from A, B and C to the opposite sides, then

OA = 2R cos A

OB = 2R cos B

OC = 2R cos C

The circum radius of the pedal triangle = R/2

The area of the pedal triangle is = 2Δ cos A cos B cos C
Some Important Results:

tan A/2 tan B/2 = (s-c)/s

tan A/2 + tan B/2 = c/s cot C/2 = c(s-c)/Δ

tan A/2 - tan B/2 = (a-b)(s-c)/Δ

cot A/2 + cot B/2 = (tan A/2 + tan B/2)/ (tan A/2.tan B/2)

= c/(s-c) cot C/2 ओपन / कमेंट

2021-06-27 17:19:04 STRUCTURE OF HUMAN HEART AND CARDIAC CYCLE

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2021-06-27 17:18:55
ELECTROMAGNETIC INDUCTION SHORT NOTES

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