Embibe Experts Solutions for Chapter: Triangles, Exercise 1: Karnataka Board-2019

Draw a chord of length $6 cm$ in a circle of radius $5 cm$. Measure and write the distance of the chord from the centre of the circle.

In $∆ ABC$, $\angle ABC=90°$, $BD\perp AC$. If $BD=8 cm$, $AD=4 cm$, find $CD$ and $AB$.

In $∆ ABC$, $XY\parallel BC$ and, $XY=\frac{1}{2}BC$. If the area of $∆AXY=10 c{m}^2$, find the area of trapezium $XYCB$.

In $△ABC$, $AD$ is drawn perpendicular to $BC$. If $BD:CD=3:1$, then prove that $B{C}^2=2\left(A{B}^2-A{C}^2\right)$.

In the $△ \mathrm{ABC}$, if $\mathrm{DE} \left|\right| \mathrm{AC}$, then the correct relation is

The diagonal of a rectangular playground is $60 \mathrm{m}$ more than the smaller side of the rectangle. If the longer side is $30 \mathrm{m}$ more than the smaller side, find the sides of the playground.

In the $△ABD$, $C$ is a point on $BD$ such that $BC: CD=1: 2$, and $△ABC$ is an equilateral triangle. Then prove that $A{D}^2=7A{C}^2$.

Prove that ''if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar''.