Question : In the given figure, a circle is inscribed in $\triangle$PQR, such that it touches the sides PQ, QR and RP, at points D, E, and F, respectively. If the lengths of the sides PQ = 18 cm, QR = 13 cm, and RP = 15 cm, find the length of PD.
Option 1: 10 cm
Option 2: 8 cm
Option 3: 15 cm
Option 4: 12 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: PQ = 18 cm, QR = 13 cm, and RP = 15 cm We know that two tangents to a circle from the same external point are equal. So, PF = PD Let the length of PD be $x$. DQ = $18-x$ = EQ FR = $15-x$ = RE Now, QR = RE + EQ ⇒ $13=15-x+18-x$ ⇒ $2x=33-13$ $\therefore x =10$ Hence, the correct answer is 10 cm.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : A circle is inscribed in $\triangle $PQR touching the sides QR, PR and PQ at the points S, U and T, respectively. PQ = (QR + 5) cm, PQ = (PR + 2) cm. If the perimeter of $\triangle $PQR is 32 cm, then PR is equal to:
Question : If $\triangle ABC \sim \triangle PQR$, AB =4 cm, PQ=6 cm, QR=9 cm and RP =12 cm, then find the perimeter of $\triangle$ ABC.
Question : O is the centre of this circle. Tangent drawn from a point P, touches the circle at Q. If PQ = 24 cm and OQ = 10 cm, then what is the value of OP?
Question : $\triangle BAC\sim \triangle PQR$. The area of $\triangle BAC$ and $\triangle PQR$ is 25 cm2 and 36 cm2 respectively. If BA = 4 cm, then what is the length of PQ?
Question : Let A, B, and C be the mid-points of sides PQ, QR, and PR, respectively, of PQR. If the area of $\triangle$ PQR is 32 cm2, then find the area of $\triangle$ ABC.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile