In the given figure, \(\triangle ACB={ 90 }^{ ° }\) and \(CD\bot AB\) . Prove that \(\frac { { BC }^{ 2 } }{ { AC }^{ 2 } } =\frac { BD }{ AD } \)

2

(a)

A girl of height 100 cm is walking away from the base of a lamppost at a speed of 1.9 m/s. If the lamp is 5 m above the ground, find the length of her shadow after 4s.
 

2

(a)

In an equilateral triangle of side\(3\sqrt { 3 } cm,\) find the length of the altitude.

2

(a)

In the given figure, OA = 3 cm, OB = 4 cm, \(\angle\)AOB = 90\(\unicode{xb0} \), AC = 12 cm and BC = 13 cm, prove that \(\angle\)CAB = 90\(\unicode{xb0} \).

2

(a)

In an equilateral triangle of side 24 cm, find the length of the altitude.

2

(a)

In the given figure, DE || BC. If AD=1.5 cm, BD=2AD, then find \(\frac { ar(\triangle ABC) }{ ar(trapeziumBCED) } .\)

2

(a)

In the given triangle PQR, \(\angle\)OPR = 90\(\unicode{xb0} \), PQ = 24 cm and QR = 26 cm and in PKR, \(\angle\)PKR = 90\(\unicode{xb0} \) and KR = 8 cm, find PK.

2

(a)

In the given figure, in a triangle PQR, ST || QR and \(\frac { PS }{ SQ } =\frac { 3 }{ 5 } \) and PR=28 cm, find PT.

2

(a)

In the given figure, if ABCD is a trapezium in which AB || CD || EF, then prove that \(\frac { AE }{ ED } =\frac { BF }{ FC } .\)

2

(a)

In the given figure, find the measure of \(\angle\)X.

2

(a)

ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that \(\frac { AO }{ BO } =\frac { CO }{ DO } .\)

2

(a)

In the given figure, PQR is a triangle right angled at Q and XY || QR. If PQ=6 cm, PY=4 cm and PX : XQ=1 : 2. Calculate the lengths of PR and QR.

2

(a)

In the given figure, OA . OB = OC . OD. Show that \(\angle\)A = \(\angle\)C and \(\angle\)B = \(\angle\)D.

2

(a)

In the given figure, if AB II DC, find the value of x.

2

(a)

In the given figure, CB II QR and CA II PR. If AQ = 12 cm, AR = 20 cm, PB = CQ = 15 cm, calculate PC and BR.

2

(a)