What is the relationship between Km and m?

Tutorialspoint

Simply Easy Learning

---

Updated on 10-Oct-2022 09:40:07

0 Views

Print Article

• Related Articles
• 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 \( A B \).
• Simplify the following.a) \( (l^{2}-m^{2})(2 l+m)-m^{3} \)b) \( (p+q+r)(p-q+r)+p q-q r \)
• 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 \( \triangle A B C, \angle A \) is obtuse, \( P B \perp A C, \) and \( Q C \perp A B \). Prove that \( B C^{2}=\left(A C \times C P +A B \times B Q\right) \).
• 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.
• From an external point \( P \), tangents \( P A=P B \) are drawn to a circle with centre \( O \). If \( \angle P A B=50^{\circ} \), then find \( \angle A O B \).
• In \( \triangle A B C, \angle A \) is obtuse, \( P B \perp A C, \) and \( Q C \perp A B \). Prove that \( A B \times A Q=A C \times A P \).
• 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 \( O P=2 A P \).
• Prove that the points $P( a,\ b+c),\ Q( b,\ c+a)$ and $R( c,\ a+b)$ are Collinear.
• Find the value of:(a) \( 4.9 \p 0.07 \)(b) \( 26.4 \p 2.4 \)
• 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
• If $a = xy^{p-1}, b = xy^{q-1}$ and $c = xy^{r-1}$, prove that $a^{q-r} b^{r-p} c^{p-q} = 1$.
• Solve the following pairs of linear equations: (i) \( p x+q y=p-q \)$q x-p y=p+q$(ii) \( a x+b y=c \)$b x+a y=1+c$,b>(iii) \( \frac{x}{a}-\frac{y}{b}=0 \)$a x+b y=a^{2}+b^{2}$(iv) \( (a-b) x+(a+b) y=a^{2}-2 a b-b^{2} \)$(a+b)(x+y)=a^{2}+b^{2}$(v) \( 152 x-378 y=-74 \)$-378 x+152 y=-604$.
• <p>When a <b>sportsman</b> runs, he often gets <b>muscle cramps</b>. Give reason.</p>
• A point $A( 0,\ 2)$ is equidistant from the points $B( 3,\ p)$ and $C( p,\ 5)$, then find the value of P.