(C) In a right-angled triangle $\Delta ABC$ where $\angle B = 90^{\circ}$,if $\overline{BM}$ is the altitude to the hypotenuse $AC$,then by the proper

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

(C) In a right-angled triangle $\Delta ABC$ where $\angle B = 90^{\circ}$,if $\overline{BM}$ is the altitude to the hypotenuse $AC$,then by the properties of similar triangles $(\Delta BMC \sim \Delta BCA)$:$\frac{BC}{AC} = \frac{MC}{BC}$Cross-multiplying gives:$BC^2 = MC \cdot AC$This implies that $BC$ is the geometric mean of $CM$ and $AC$.

Class 10 Mathematics Triangles Mix Examples - Triangles

Medium

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $AC$. Then,$BC$ is the geometric mean of..........

A
$BM$ and $AC$
B
$AM$ and $CM$
C
$CM$ and $AC$
D
$AM$ and $AC$

Explore More

Browse All

Question Bank

All Subjects

Class 10 Questions

Class 10

Mathematics Questions

Chapter

Triangles

Subtopic

Mix Examples - Triangles

In $\Delta ABC$,$m\angle B = 90^\circ$. If $AB = 12$ and $BC = 5$,then $AC = \dots$

Medium

View Solution

$\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow XZY$. If $PQ = 8$,$XZ = 12$ and the area of $\Delta PQR$ is $24$,find the area of $\Delta XYZ$.

Medium

View Solution

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at point $D$,then

Medium

View Solution

In $\Delta PQR, m \angle Q = 90^{\circ}$. If $PR = 17$ and $PQ = 8$,then $QR = \ldots$

Medium

View Solution

In $\Delta XYZ$,$m\angle Y = 90^{\circ}$ and $\overline{YM}$ is an altitude to the hypotenuse $\overline{XZ}$. If $YM = 12$ and $XM = 8$,find $XZ$.

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $AC$. Then,$BC$ is the geometric mean of..........

Similar Questions

In $\Delta ABC$,$m\angle B = 90^\circ$. If $AB = 12$ and $BC = 5$,then $AC = \dots$

$\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow XZY$. If $PQ = 8$,$XZ = 12$ and the area of $\Delta PQR$ is $24$,find the area of $\Delta XYZ$.

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at point $D$,then

In $\Delta PQR, m \angle Q = 90^{\circ}$. If $PR = 17$ and $PQ = 8$,then $QR = \ldots$

In $\Delta XYZ$,$m\angle Y = 90^{\circ}$ and $\overline{YM}$ is an altitude to the hypotenuse $\overline{XZ}$. If $YM = 12$ and $XM = 8$,find $XZ$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module