Pedal Triangle

Q. The area of an acute triangle $ABC$ is $\Delta$, the area of its pedal triangle is '$p$', where $\cos B=\frac{2p}{\Delta }$ and $\sin B=\frac{2\sqrt{3}p}{\Delta }$. The value of $8({\cos }^{2}A\cos B+{\cos }^{2}C)$ is

1. $1$
2. $2$
3. $3$
4. $4$

Q. In an acute angled triangle ABC, D, E and F are the feets of perpendiculars from A, B and C respectively and H is the orthocenter.
$\mathrm{If}\sin A=\frac{3}{5}\mathrm{and}\mathrm{BC}=39,\mathrm{then}\mathrm{length}\mathrm{of}\mathrm{AH}=$
.

1. 52
2. 65
3. 26
4. 39

Q. The area of an acute triangle $ABC$ is $\Delta$, the area of its pedal triangle is '$p$', where $\cos B=\frac{2p}{\Delta }$ and $\sin B=\frac{2\sqrt{3}p}{\Delta }$. The value of $8({\cos }^{2}A\cos B+{\cos }^{2}C)$ is

1. $1$
2. $2$
3. $3$
4. $4$

Q. In an acute angled triangle ABC, D, E and F are the feets of perpendiculars from A, B and C respectively and H is the orthocenter.
$\mathrm{If}\sin A=\frac{3}{5}\mathrm{and}\mathrm{BC}=39,\mathrm{then}\mathrm{length}\mathrm{of}\mathrm{AH}=$
.

1. 52
2. 65
3. 26
4. 39