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.
Sunday, 18 August 2019
Sunday, 26 May 2019
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.
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.
Saturday, 20 April 2019
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.
Sunday, 7 April 2019
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.
(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.
Sunday, 31 March 2019
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