In Delta XYZ,the bisector of angle X intersec | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) In $\Delta XYZ$,$XM$ is the bisector of $\angle X$,which intersects $\overline{YZ}$ at $M$.According to the Angle Bisector Theorem,the ratio of th

Vedclass · Accepted Answer

$9.8$

Vedclass · Answer

(B) In $\Delta XYZ$,$XM$ is the bisector of $\angle X$,which intersects $\overline{YZ}$ at $M$.According to the Angle Bisector Theorem,the ratio of the sides forming the angle is equal to the ratio of the segments of the opposite side.$	herefore \frac{XY}{XZ} = \frac{YM}{MZ}$Substituting the given values:$	herefore \frac{6}{8} = \frac{4.2}{MZ}$$	herefore MZ = \frac{4.2 	imes 8}{6}$$	herefore MZ = 0.7 	imes 8 = 5.6$Now,$YZ = YM + MZ$ (since $Y-M-Z$ are collinear).$YZ = 4.2 + 5.6 = 9.8$.

Part $I$	Part $II$
$1.$ In $\Delta ABC, AB=3, BC=4, AC=5$	$a.$ In-radius $= 1$
$2.$ In $\Delta PQR, PQ=5, QR=12, PR=13$	$b.$ In-radius $= 2$
$3.$ In $\Delta XYZ, XY=8, YZ=15, XZ=17$	$c.$ In-radius $= 3$
$4.$ In $\Delta MNP, MN=20, NP=21, MP=29$	$d.$ In-radius $= 6$

In $\Delta XYZ$,the bisector of $\angle X$ intersects $\overline{YZ}$ at $M$. If $XY = 6$,$XZ = 8$ and $YM = 4.2$,find $YZ$.

Similar Questions

The perimeter of rhombus $ABCD$ is $116$. If $AC = 42$, find $BD$.

In the given figure,if $\angle 1 = \angle 2$ and $\triangle NSQ \cong \triangle MTR,$ then prove that $\triangle PTS \sim \triangle PRQ.$

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QM}$ is an altitude. If $PQ = 40$ and $QR = 30$,find the area of $\Delta QMR$.

In $\Delta XYZ$,$\overline{XN}$ is a median. If $XY^2 + XZ^2 = 200$ and $XN = 8$,find $YZ$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module