M L Aggarwal Solutions for Chapter: Triangles, Exercise 3: Execise 7.3

In the adjoining figure, $\angle A=90°$ and $AD\perp BC$. If $BD=2 \mathrm{cm}$, $CD=8 \mathrm{cm}$ and $AD=k \mathrm{cm}$, find $k$.

In the adjoining figure, two chords $AB$ and $CD$ intersect each other at the point $P$ (when produced) outside the circle. Prove that $△PAC~△PDB$.

In the adjoining figure, two chords $AB$ and $CD$ intersect each other at the point $P$ (when produced) outside the circle. Prove that $PA\times PB=PC\times PD$.

In the adjoining figure, $CM$ and $RN$ are respectively the medians of $△ABC$ and $△PQR$. If $△ABC~△PQR$, prove that: $△AMC~△PNR$.

In the adjoining figure, $CM$ and $RN$ are respectively the medians of $△ABC$ and $△PQR$. If $△ABC~△PQR$, prove that: $\frac{CM}{RN}=\frac{AB}{PQ}$.

In the adjoining figure, $CM$ and $RN$ are respectively the medians of $△ABC$ and $△PQR$. If $△ABC~△PQR$, prove that: $△CMB~△RNQ$.

A $15$ metres high tower casts a shadow of $24$ metres long at a certain time and at the same time, a telephone pole casts a shadow $16$ metres long. If the height of the telephone pole is $x \mathrm{m}$, find $x$.

A street light bulb is fixed on a pole $6 \mathrm{m}$ above the level of street. If a woman of height $1.5 \mathrm{m}$ casts a shadow of $3 \mathrm{m}$,  and she is $x \mathrm{m}$ away from the base of the pole, find $x$.