Question : A circle is inscribed in a ΔABC having sides AB = 16 cm, BC = 20 cm, and AC = 24 cm, and sides AB, BC, and AC touch circle at D, E, and F, respectively. The measure of AD is:
Option 1: 10 cm
Option 2: 20 cm
Option 3: 6 cm
Option 4: 14 cm
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 10 cm
Solution :
Given: A circle is inscribed in a ΔABC having sides AB = 16 cm, BC = 20 cm, and AC = 24 cm, and sides AB, BC, and AC touch circle at D, E, and F, respectively. We know that tangents drawn from an external point to a circle are equal in length. Let AD = AF = a, BD = BE = b and CE = CF = c According to the question, AB = a + b ⇒ 16 = a + b .......(1) BC = b + c ⇒ 20 = b + c .......(2) AC = a + c ⇒ 24 = a + c .......(3) Now, On adding equations (1), (2), and (3), we get ⇒ 16 + 20 + 24 = a + b + b + c + a + c ⇒ 60 = 2(a + b + c) ⇒ a + b + c = 30 Now putting the value of (b + c) in the above equation, ⇒ a + 20 = 30 ⇒ a = 10 cm Hence, the correct answer is 10 cm.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : ABC is an isosceles triangle inscribed in a circle. If AB = AC = $12\sqrt{5}$ cm and BC = 24 cm, then the radius of circle is:
Question : A circle touches all four sides of a quadrilateral ABCD. If AB = 18 cm, BC = 21 cm, and AD = 15 cm, then length CD is:
Question : In $\triangle ABC$, D and E are points on the sides AB and AC, respectively, such that DE || BC. If AD = 5 cm, DB = 9 cm, AE = 4 cm, and BC = 15.4 cm, then the sum of the lengths of DE and EC (in cm) is:
Question : If $D$ and $E$ are points on sides $AB$ and $AC$ of $\Delta ABC$. $DE$ is parallel to $BC$. If $AD: DB = 2:3$ and the area of $\Delta ADE$ is 4 sq. cm, what is the area (in sq. cm) of quadrilateral $BDEC$?
Question : In $\triangle ABC$, D and E are the midpoints of sides BC and AC, respectively. AD and BE intersect at G at the right angle. If AD = 18 cm and BE=12 cm, then the length of DC (in cm ) is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile