A boy of height 90cm is walking away from the base of a lamp post at a speed of 1.2m/sec. If the lamppost is 3.6m above the ground, find the length of his shadow cast after 4 seconds.

Two poles of height ‘a’ metres and ‘b’ metres are ‘p’ metres apart. Prove that the height of the point of intersection of the lines joining the top of each pole to the foot of the opposite pole is given by \(\frac { ab }{ a+b } \) meters

A girl looks the reflection of the top of the lamp post on the mirror which is 6.6 m away from the foot of the lamp post. The girl whose height is 12.5 m is standing 2.5 m away from the mirror. Assuming the mirror is placed on the ground facing the sky and the girl, mirror and the lamp post are in a same line, find the height of the lamp post.

If \(\triangle\)ABC~\(\triangle\)DEF such that area of \(\triangle\)ABC is 9cm² and the area of \(\triangle\)DEF is 16cm² and BC = 2.1 cm. Find the length of EF

Two vertical poles of heights 6 m and 3 m are erected above a horizontal ground AC. Find the value of y.

In \(\triangle\) ABC, if DE||BC, AD = x, DB = x − 2, AE = x +2 and EC = x − 1 then find the lengths of the sides AB and AC.

In the figure DE||AC and DC||AP. Prove that \(\frac { BE }{ CE } =\frac { BC }{ CP } \)

Construct a \(\triangle\)PQR in which PQ = 8 cm, \(\angle\)R = 60^o and the median RG from R to PQ is 5.8 cm. Find the length of the altitude from R to PQ.

Construct a triangle \(\triangle\)PQR such that QR = 5 cm, \(\angle\)P = 30^o and the altitude from P to QR is of length 4.2 cm.

In \(\triangle\)ABC,D and E are points on the sides AB and AC respectively such that DE||BC \(\frac { AD }{ DB } =\frac { 3 }{ 4 } \) and AC = 15cm find AE.

Rhombus \(\triangle\)QRB is inscribed in \(\triangle\)ABC such that \(\angle\)B is one of its angle. P, Q and R lie on AB, AC and BC respectively. If AB = 12 cm and BC = 6 cm, find the sides PQ, RB of the rhombus.

In trapezium ABCD, AB || DC, E and F are points on non-parallel sides AD and BC respectively, such that EF || AB. Show that \(\frac { AE }{ ED } =\frac { BF }{ FC } \)

In figure DE || BC and CD. Prove that AD² = AB x AF

In figure \(\angle\)QPR = 90^o, PS is its bisector. If ST\(\bot \)PR, prove that ST \(\times\) (PQ + PR) = PQ \(\times\) PR.

ABCD is a quadrilateral in which AB=AD, the bisector of \(\angle\)BAC and \(\angle\)CAD intersect the sides BC and CD at the points E and F respectively. Prove that EF||BD

P and Q are the mid-points of the sides CA and CB respectively of a \(\triangle\)ABC, right angled at C. Prove that 4(AQ² + BP²) = 5AB²

An Aeroplane after take off from an airport and flies due north at a speed of 1000 km/hr. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km/hr. How far apart will be the two planes after 1½ hours?

There are two paths that one can choose to go from Sarah’s house to James house. One way is to take C street, and the other way requires to take B street and then A street. How much shorter is the direct path along C street? (Using figure).

To get from point A to point B you must avoid walking through a pond. You must walk 34 m south and 41 m east. To the nearest meter, how many meters would be saved if it were possible to make a way through the pond?

5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall

The perpendicular PS on the base QR of a \(\triangle\)PQR intersects QR at S, such that QS = 3 SR. Prove that 2PQ² = 2PR² + QR²

In the adjacent figure, ABC is a right angled triangle with right angle at B and points D, E trisect BC. Prove that 8AE² = 3AC² + 5AD²

PQ is a chord of length 8 cm to a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length of the tangent TP.

Show that in a triangle, the medians are concurrent.

In Fig, ABC is a triangle with \(\angle\)B=90^o, BC=3cm and AB=4 cm. D is point on AC such that AD=1 cm and E is the midpoint of AB. Join D and E and extend DE to meet CB at F. Find BF.

In \(\triangle\)ABC , points D,E,F lies on BC, CA, AB respectively. Suppose AB, AC and BC have lengths 13, 14 and 15 respectively. If \(\frac { AF }{ FB } =\frac { 2 }{ 5 } \quad \frac { CE }{ EA } =\frac { 5 }{ 8 } \). Find BD an DC 

In a garden containing several trees, three particular trees P, Q, R are located in the following way, BP = 2 m, CQ = 3 m, RA = 10 m, PC = 6 m, QA = 5 m, RB = 2 m, where A, B, C are points such that P lies on BC, Q lies on AC and R lies on AB. Check whether the trees P, Q, R lie on a same straight line.

In figure, O is the centre of the circle with radius 5 cm. T is a point such that OT = 13 cm and OT intersects the circle E, if AB is the tangent to the circle at E, find the length of AB

Show that the angle bisectors of a triangle are concurrent.

In \(\triangle\)ABC , with \(\angle\)B=90° , BC = 6 cm and AB = 8 cm, D is a point on AC such that AD = 2 cm and E is the midpoint of AB. Join D to E and extend it to meet at F. Find BF.

An artist has created a triangular stained glass window and has one strip of small length left before completing the window. She needs to figure out the length of left out portion based on the lengths of the other sides as shown in the figure.

In the given figure AB || CD || EF. If AB = 6cm, CD = x cm, EF = 4 cm, BD = 5 cm and DE = y can. Final x and y

O is any point inside a triangle ABC. The bisector of \(\angle AOB\), \(\angle BOC\) and \(\angle COA\) meet the sides AB, BC and CA in point D, E and F respectively. Show that AD x BE x CF = DB x EC x FA

In the figure, ABC is a triangle in which AB = AC. Points D and E are points on the side AB and AC respectively such that AD =  AE. Show that the points B, C, E and D lie on a same circle.

Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of 20 km/hr and the second train travels at 30 km/hr. After 2 hours, what is the distance between them?

A man whose eye-level is 2 m above the ground wishes to find the height of a tree. He places a mirror horizontally on the ground 20 m from the tree and finds that if he stands at a point C which is 4 m from the mirror B, he can see the reflection of the top of the tree. How height is the tree?

An Emu which is 8 feet tall is standing at the foot of a pillar which is 30 feet high. It walks away from the pillar. The shadow of the Emu falls beyond Emu. What is the relation between the length of the shadow and the distance from the Emu to the pillar?

Two circles intersect at A and B. From a point P on one of the circles lines PAC and PBD are drawn intersecting the second circle at C and D. Prove that CD is parallel to the tangent at P.

Let ABC be a triangle and D,E,F are points on the respective sides AB, BC, AC (or their extensions). Let AD:DB = 5 : 3, BE : EC = 3 : 2 and AC = 21. Find the length of the line segment CF.

In \(\triangle\)ABC, D and E are points on the sides AB and AC respectively such that DE||BC
If AD = 8x - 7, DB = 5x - 3, AE = 4x - 3, and EC = 3x - 1, find the value of x.

Basic Proportionality Theorem (BPT) or State and prove Thales theorem?

Converse of Angle Bisector Theorem

Pythagoras Theorem

State the Alternate Segment theorem

State and Prove - Angle Bisector Theorem

Converse of Basic Proportionality Theorem