Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Geometry

Question:

D is a point on the side BC of a $\triangle$ABC such that $\angle ADC = \angle BAC$. If CA = 10 cm and BC = 16 cm then the length of CD is:

Options:

6 cm

6.5 cm

6.25 cm

7 cm

Correct Answer:

6.25 cm

Explanation:

\(\Delta \)DCA is similar to \(\Delta \)ACB

\(\frac{CD}{AC}\) = \(\frac{AC}{BC}\)

= \(\frac{CD}{AC}\) = \(\frac{10}{16}\)

= CD = \(\frac{10 \;×\; 10}{16}\) = 6.25 cm.