Expalnation required (Question:869543.0)

Online Courses

Test Series

Resources

Offline Courses

Community

+91 7676564400

support@toprankers.com

Mobile App

Mock Tests

Practice

Assignment

Study Notes

SSC Articles

Discussions

Online Coaching

GK- Current Affairs

Bookmarked Questions

Descriptive Papers

Discussions

Select Date

Tags:

Submit Discussion

sai charan

· started a discussion

· 1 Months ago

Expalnation required (Question:869543.0)

r1 is 6, r2 is 8
so PQ length is 8+6 = 14

Question:

In the given figure, ACB is a right angled triangle. CD is the altitude. Circles are inscribed within the $Δ A C D$ and $Δ B C D$ .P and Q are the centers of the circles. The distance PQ is:

Options:

$\sqrt{150}$

$\sqrt{50}$

$10 \sqrt{2}$

Solution:

In right angle $Δ A B C$ ,

AB = $\sqrt{3 0^{2} + 4 0^{2}}$ = 50cm

And CD = $\frac{30 \times 40}{50}$ = 24cm

In right angle $Δ A C D$ ,

AD = $\sqrt{3 0^{2} - 2 4^{2}}$ = 18cm

In right angle $Δ B C D$

$B D = \sqrt{4 0^{2} - 2 4^{2}}$ = 32 cm

In radius of $Δ A C D$ ,

r₁ = $\frac{P + B - H}{2} = \frac{18 + 24 - 30}{2}$ = 6cm

and in radius of $Δ C D B$

r₂ = $\frac{P + B - H}{2} = \frac{24 + 32 - 40}{2}$ = 8cm

In $Δ$ PQM,

$∴ P Q = \sqrt{1 4^{2} + 2^{2}} = \sqrt{200}$ = $10 \sqrt{2}$ cm

We at aim to provide most comprehensive content & test for practice which is carefully divided into various chapters and topics to help you focus on your weak areas.Our Practice mock test gives you unmatched analytics to help you realize your strong areas,time management and improvement areas.Our Short & Crisp notes on each topic will help you to quickly revise the topic along with the tips & tricks of the exams.

More About