How will you prove that soil contains air in it?

Tutorialspoint

Simply Easy Learning

---

Updated on 10-Oct-2022 12:40:42

0 Views

Print Article

• Related Articles
• Two tangent segments \( P A \) and \( P B \) are drawn to a circle with centre \( O \) such that \( \angle A P B=120^{\circ} . \) Prove that \( O P=2 A P \).
• If $a = xy^{p-1}, b = xy^{q-1}$ and $c = xy^{r-1}$, prove that $a^{q-r} b^{r-p} c^{p-q} = 1$.
• Draw a line segment \( A B=5.5 \mathrm{cm} \). Find a point \( P \) on it such that \( \overline{A P}=\frac{2}{3} \overline{P B} \).
• Prove that the points $P( a,\ b+c),\ Q( b,\ c+a)$ and $R( c,\ a+b)$ are Collinear.
• In \( \triangle A B C, \angle A \) is obtuse, \( P B \perp A C, \) and \( Q C \perp A B \). Prove that \( A B \times A Q=A C \times A P \).
• If \( P A \) and \( P B \) are tangents from an outside point \( P \). such that \( P A=10 \mathrm{~cm} \) and \( \angle A P B=60^{\circ} \). Find the length of chord \( A B \).
• In the adjoining figure, $P R=S Q$ and $S R=P Q$.a) Prove that $\angle P=\angle S$.b) $\Delta SOQ \cong \Delta POR$."\n
• In \( \triangle A B C, \angle A \) is obtuse, \( P B \perp A C, \) and \( Q C \perp A B \). Prove that \( B C^{2}=\left(A C \times C P +A B \times B Q\right) \).
• How will you show that air supports burning?
• If the point $P( x,\ y)$ is equidistant from the points $A( a\ +\ b,\ b\ –\ a)$ and $B( a\ –\ b,\ a\ +\ b)$. Prove that $bx=ay$.
• In the figure, \(P A \) and \( P B \) are tangents from an external point \( P \) to a circle with centre \( O \). \( L N \) touches the circle at \( M \). Prove that \( P L+L M=P N+M N \)."\n
• From a point \( P \), two tangents \( P A \) and \( P B \) are drawn to a circle with centre \( O \). If \( O P= \) diameter of the circle, show that \( \Delta A P B \) is equilateral.
• Prove that for any prime positive integer $p$, $\sqrt{p}$ is an irrational number.
• Prove that $\sqrt{p} + \sqrt{q}$ is irrational, where $p$ and $q$ are primes.
• How will you show that air is dissolved in water?