Question : The radius of the incircle of a triangle whose sides are 9 cm, 12 cm, and 15 cm is:
Option 1: 9 cm
Option 2: 13 cm
Option 3: 3 cm
Option 4: 6 cm
New: SSC CHSL tier 1 answer key 2024 out | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 3 cm
Solution : Checking for the triangle by using Pythagoras theorem. $9^2 + 12^2 = 15^2$ Thus, The triangle is right-angled. Given, AB = 9, BC = 12 cm OD = OE = OF = $x$ cm (radius of the circle) And, BEOD is a square. AD = AF = $9-x$ ($\because $ The length of the tangent from a point to the circle is the same.) EC = CF = $12-x$ ($\because $ The length of the tangent from a point to the circle is the same.) $\therefore$ AC = AF + FC ⇒ $9-x+12-x = 15$ ⇒ $21-2x = 15$ ⇒ $2x = 21-15$ ⇒ $2x = 6$ ⇒ $x = \frac{6}{2} = 3$ Hence, the correct answer is 3 cm.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : The base of a right prism is a right-angled triangle whose sides are 5 cm, 12 cm, and 13 cm. If the area of the total surface of the prism is 360 cm2, then its height is:
Question : The sides of a triangle are 9 cm, 6 cm, and 5 cm. What is the value of the circumradius of this triangle?
Question : The length of the diagonal of a square is $9\sqrt{2}$ cm. The square is reshaped to form an equilateral triangle. What is the area (in cm2) of the largest incircle that can be formed in that triangle?
Question : The three sides of a triangle are 7 cm, 9 cm, and 8 cm. What is the area of the triangle?
Question : The sides of a triangle are in the ratio 7 : 9 : 12. The difference between the lengths of the largest and smallest sides is 15 cm. The length of the largest side would be (in cm):
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile