1. InΔPQR, given that S is a point on PQ such that STIIQR and PS/SQ=3/5 If PR = 5.6 cm, then find PT.
2. InΔABC, AE is the external bisector of <A, meeting BC produced at E. If AB = 10 cm, AC = 6 cm and BC = 12 cm, then find CE.
3. P and Q are points on sides AB and AC respectively, ofΔABC. If AP = 3 cm,PB = 6 cm, AQ = 5 cm and QC = 10 cm, show that BC = 3 PQ.
4. The image of a tree on the film of a camera is of length 35 mm,the distancefrom the lens to the film is 42 mm andthe distancefrom the lens to the tree is 6 m. How tall is the portion of the tree being photographed?
5. D is the midpoint of the side BC ofΔABC. If P and Q are points on AB and on AC such that DP bisects <BDA and DQ bisects <ADC, then prove that PQ II BC.
6. If a straight line is drawn parallel to one side of a triangle intersecting the othertwo sides, then it divides thetwo sidesin the same ratio.
7. If a straight line divides anytwo sidesof a triangle in the same ratio, then the line must be parallel to the third side.
8. ABCD is a quadrilateral with AB =AD. If AE and AF are internal bisectors of <BAC and <DAC respectively, then prove that EF II BD. In aΔABC, D and E are points on AB and AC respectively such that AD/ DB = AEC/EC and <ADE = <DEA. Prove thatΔABC is isosceles.
9. In aΔABC, points D, E and F are taken on the sides AB, BC and CA respectively such that DE IIAC and FE II AB.
10. The internal bisector of <A ofΔABC meets BC at D and the external bisector of <A meets BC produced at E. Prove that BD/ BE = CD/CE
11. If a perpendicular is drawn from the vertex of a right angled triangle to its hypotenuse, then the triangles on each side of the perpendicular are similar to the whole triangle.
12. A man sees the top of a tower in a mirror which is at a distance of 87.6 m from the tower. The mirror is on the ground, facing upward. The man is 0.4 maway fromthe mirror, andthe distanceof his eye level from the ground is 1.5 m. How tall is the tower? (The foot of man, the mirror and the foot of the tower lie along a straight line).
13. In a rightΔABC, right angled at C, P and Q are points of the sides CA and CB respectively, which divide these sides in the ratio 2: 1. Prove that
(I) 9AQ2= 9AC2+4BC2 (II) 9 BP2= 9 BC2+ 4AC2(III) 9 (AQ2+BP2) = 13AB2
14. ABC is a triangle. PQ is the line segment intersecting AB in P and AC in Q such that PQ parallel to BC and dividesΔABC into two parts equal in area. Find BP: AB.
15. P and Q are the mid points on the sides CA and CB respectively of triangle ABC right angled at C. Prove that4(AQ2+BP2) = 5 AB2
16. In an equilateralΔABC, the side BC is trisected at D. Prove that 9AD2 = 7AB2
17. Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians ofthe triangle.
18. If ABC is an obtuse angled triangle, obtuse angled at B and if AD^CB Prove that
1.AC2=AB2+ BC2+2 BC x BD
19. Prove that in any triangle the sum of the squares of anytwo sidesis equal to twice the square of half of the third side together with twice the square of the median, which bisects the third side.
[To prove AB2+ AC2= 2AD2+ 2(1/2BC)2]
20. ABC is a right triangle right-angled at C and AC= √3 BC. Prove that <ABC=60o
Let ABC be triangle and D and E be two pobcints on side AB such that AD=BE. if DP||BC and EQ||AC, then prove PQ||AB
prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see given figure). Find the sides AB and AC.
explain this some in a little easy maNNER.PLS EXPERTSS
if(-4,3)and(4,3)are two vertices of an equilateral triangle. find the coordinates of the third vertex. given that the origin lies in the interior of the triangle.
How to prove three points collinear by Section Formula
ABC is a right triangle right angled at B, such that BC = 6 cm and AB = 8 CM, find the radius of its in circle.
prove that root 2+ root 3 is an irrational number
a cone of radius 10 cm is divided into two parts by drawing a plane through the midpoint of its axis , parallel to its base . compare the volume of the two parts
a farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field , which is 10m in diameter and 2 m deep. If water flows through the pipe at the rate of 3km/hr , in how much time the tank be filled ?
how to solve (a-b)x + (a+b)y = (a2-2ab-b2) , (a+b) (x+y)=a2+b2. by cross multiplication method
If a sin theta + b cos theta = c , then prove that a cos theta - b sin theta = the whole under root a2 + b2 - c2 .
plz answer soon if u want a thumbzzzz up guys !!!!!!!!!!!!!
If alpha and beta are the zeros of polynomial x2 - 5x + k such that alpha-beta=1. find the value of k ......
1. InΔPQR, given that S is a point on PQ such that STIIQR and PS/SQ=3/5 If PR = 5.6 cm, then find PT.
2. InΔABC, AE is the external bisector of <A, meeting BC produced at E. If AB = 10 cm, AC = 6 cm and BC = 12 cm, then find CE.
3. P and Q are points on sides AB and AC respectively, ofΔABC. If AP = 3 cm,PB = 6 cm, AQ = 5 cm and QC = 10 cm, show that BC = 3 PQ.
4. The image of a tree on the film of a camera is of length 35 mm,the distancefrom the lens to the film is 42 mm andthe distancefrom the lens to the tree is 6 m. How tall is the portion of the tree being photographed?
5. D is the midpoint of the side BC ofΔABC. If P and Q are points on AB and on AC such that DP bisects <BDA and DQ bisects <ADC, then prove that PQ II BC.
6. If a straight line is drawn parallel to one side of a triangle intersecting the othertwo sides, then it divides thetwo sidesin the same ratio.
7. If a straight line divides anytwo sidesof a triangle in the same ratio, then the line must be parallel to the third side.
8. ABCD is a quadrilateral with AB =AD. If AE and AF are internal bisectors of <BAC and <DAC respectively, then prove that EF II BD. In aΔABC, D and E are points on AB and AC respectively such that AD/ DB = AEC/EC and <ADE = <DEA. Prove thatΔABC is isosceles.
9. In aΔABC, points D, E and F are taken on the sides AB, BC and CA respectively such that DE IIAC and FE II AB.
10. The internal bisector of <A ofΔABC meets BC at D and the external bisector of <A meets BC produced at E. Prove that BD/ BE = CD/CE
11. If a perpendicular is drawn from the vertex of a right angled triangle to its hypotenuse, then the triangles on each side of the perpendicular are similar to the whole triangle.
12. A man sees the top of a tower in a mirror which is at a distance of 87.6 m from the tower. The mirror is on the ground, facing upward. The man is 0.4 maway fromthe mirror, andthe distanceof his eye level from the ground is 1.5 m. How tall is the tower? (The foot of man, the mirror and the foot of the tower lie along a straight line).
13. In a rightΔABC, right angled at C, P and Q are points of the sides CA and CB respectively, which divide these sides in the ratio 2: 1. Prove that
(I) 9AQ2= 9AC2+4BC2 (II) 9 BP2= 9 BC2+ 4AC2(III) 9 (AQ2+BP2) = 13AB2
14. ABC is a triangle. PQ is the line segment intersecting AB in P and AC in Q such that PQ parallel to BC and dividesΔABC into two parts equal in area. Find BP: AB.
15. P and Q are the mid points on the sides CA and CB respectively of triangle ABC right angled at C. Prove that4(AQ2+BP2) = 5 AB2
16. In an equilateralΔABC, the side BC is trisected at D. Prove that 9AD2 = 7AB2
17. Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians ofthe triangle.
18. If ABC is an obtuse angled triangle, obtuse angled at B and if AD^CB Prove that
1.AC2=AB2+ BC2+2 BC x BD
19. Prove that in any triangle the sum of the squares of anytwo sidesis equal to twice the square of half of the third side together with twice the square of the median, which bisects the third side.
[To prove AB2+ AC2= 2AD2+ 2(1/2BC)2]
20. ABC is a right triangle right-angled at C and AC= √3 BC. Prove that <ABC=60o
Let ABC be triangle and D and E be two pobcints on side AB such that AD=BE. if DP||BC and EQ||AC, then prove PQ||AB
prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see given figure). Find the sides AB and AC.
explain this some in a little easy maNNER.PLS EXPERTSS
if(-4,3)and(4,3)are two vertices of an equilateral triangle. find the coordinates of the third vertex. given that the origin lies in the interior of the triangle.
How to prove three points collinear by Section Formula
ABC is a right triangle right angled at B, such that BC = 6 cm and AB = 8 CM, find the radius of its in circle.
prove that root 2+ root 3 is an irrational number
a cone of radius 10 cm is divided into two parts by drawing a plane through the midpoint of its axis , parallel to its base . compare the volume of the two parts
a farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field , which is 10m in diameter and 2 m deep. If water flows through the pipe at the rate of 3km/hr , in how much time the tank be filled ?
how to solve (a-b)x + (a+b)y = (a2-2ab-b2) , (a+b) (x+y)=a2+b2. by cross multiplication method
If a sin theta + b cos theta = c , then prove that a cos theta - b sin theta = the whole under root a2 + b2 - c2 .
plz answer soon if u want a thumbzzzz up guys !!!!!!!!!!!!!
If alpha and beta are the zeros of polynomial x2 - 5x + k such that alpha-beta=1. find the value of k ......