Angle bisector practice sum

In Triangle PQR, PQ=48 cm, PR=80 cm and QR= 112 cm. If PA, QB and RC are angle bisectors of interior angles P, Q and R respectively then find:
(i) QA, AR
(ii) PB, BR
(iii) PC, CQ.

H.O.T.S. Similarity and Co-ordinate Geometry

In triangle OAB if O (0,0) B (220,0), AO=77 mm & AB=165 mm. Bisector of angle OAB meets OB at C. Find coordinates of point C.

3 Sums on triangle : Similarity, Isosceles and condition for such sums

Condition: Theta1 + Theta2 < 90 deg.

The inner triangle will be isosceles triangle.

Medians divide a triangle into 6 Triangles of equal area.

(Compiled).

Square root by long division method

4299								18481401				99999999	OK	OK	OK	OK	OK	OK			Step1
												4	2	9	8	9	9	2			0	0	0		Step 3
Step 1		4										18	48	14	1	0	0	0			1	1	1		a=	42
	+	4									-	16									2	4	2		b=	9	10
Step 2		8	2									2	48								3	9	3		20a	840	10.01667
+	+		2										248								4	16	4		b=	9
Step 3			84	9	84	Tally						-	164								5	25	5		20a +b	849
		+		9									84	14							6	36	6		(20a+b)b	7641	OK
Step 4				858	8	858			Tally					8414							7	49	7
			+		8								-	7641							8	64	8		Step 4
Step 5					8596	9								773	1						9	81	9		a=	429
				+		9									77301							100			b=	8	9
Step 6						85978	9							-	68768						Step2				20a	8580	9.009441
					+		9								8533	0					a=	4			b=	8
Step 7							859798	2								853300					b=	2	3		20a +b	8596
								2							-	773802					20a	80	3.1		(20a+b)b	68768	OK
								8597984								79498	0				b=	2
								=2*square root									7949800				20a +b	82
								8597984								-	7738182				(20a+b)b	164	OK		Step 5
							= 2 x	4298992									211618	0							a=	4298
								0										21161800							b=	9	9
								Correct Answer									-	17195968							20a	85960	9.92671
																		3965832							b=	9
																									20a +b	85978
																		4299							(20a+b)b	773802	OK
																					Step 6				Step 7
																					a=	42989			a=	429899
																					b=	9	9		b=	2	2
																					20a	859780	9.246319		20a	8597980	2.461253
																					b=	9			b=	2
																					20a +b	859798			20a +b	8597984
																					(20a+b)b	7738182	OK		(20a+b)b	17195968	OK

compiled trick

Sum for 10 Standard SSC CBSE or ICSE based on Similarity H.O.T.S.

Circumcenter and Circumcircle of a triangle. My sum and new construction method

Length of angle bisector of right angle in right angled triangle

In triangle BCA, /_ C =90॰ BC=a CA=b.  Bisector of /_C meets BA at D. Find length of CD. (Hint: draw BF perpendicular on CD.)

1) Find area of the triangle BCA.

2) Find hypotenuse BA.

3)Find length of perpendicular CF on hypo. BA

4) Find BD and DA by angle bisector property / theorem.

5) Find area of triangle BCD.

6) Find BF = a sin 45॰

7) From area of triangle BCD find CD. using CD as base and BF as height.

(ab x sq root 2)/(a+b)

10 SSC 2020 onward pattern Q. 5 create your two own questions

Use 1+tan sq A= sec sq A to make question.
Two rational numbers are such that their difference and reciprocal of their sums is same and equal to k. Find the numbers.

Condition for internal or external intersection of 2 chords of a circle

In a circle one chord makes two segments of a circle. If both end points of second  chord lie in only one of segments,  then the chords will intersect in the exterior of the circle. Where as, if one end of the other chord lies in one segment and the other end lies in the opposite segment then the chords will intersect in the interior of the circle. 

My sum: Based on angles, angle bisector, cyclic quadrilateral, circle

My sum: Based on angles, angle bisector, cyclic quadrilateral, circle:

In triangle ABC /_ angle ABC (i.e. /_ ABC) equal to 90°. Ray BD is bisector of angle ABC meeting AC at D.
If ray DP is angle bisector of angle ADB and ray DQ is angle bisector of angle BDC.
Prove that:
(1) DA/DC = AB/BC
(2) (AP/PB) x (BQ/QC) = DA/DC = AB/BC
(3) Find measure of angle PDQ.
(4) Prove that quadrilateral BPDQ is cyclic.
(5) Prove that if a circle is drawn through these points i.e. B,P,D and Q, PQ will be diameter of the circle.
(6) If PQ and DB intersect at X,
prove that QX/XP = QB/BP.
(7) Hence prove that, (AP/QC) x (QX/XP) = DA/DC.

For 9 std My sum on topic "Identities"

Hint: (1) Transpose the linear algebraic expressions to denominators.

For 9 std. My sum on Statistics topic

A data arranged in ascending order has four variates. The middle 2 variates are 29 and 31. Mean and range of the data are 30 & 14 respectively. Find first and fourth variates i.e. extremes in the data.

8 Std sum on area 2 dimensional mensuration

Find side of the square whose area is same as sum of area of two rectangles; one with length 41 and breadth 3, and other with respective dimensions as 23 and 2. All dimensions in same unit.

Example of inverse variation, area of triangle

In triangle ABC, AB=35, AC=75 & BC=100 cm, find
(1) Area of the triangle
(2) AP, BQ and CR if these are perpendiculars from A,B and C on their opposite sides
(3) Verify example of inverse variation.
For a given triangle, height is in inverse proprtion to base.

My sum area mensuration 2 dimensional

Please refer the attached photo.