Home
Class 7
MATHS
Take any point O in the interior of a tr...

Take any point O in the interior of a triangle `PQR.` Is (i) `OP+OQ > PQ?` (ii) `OQ+OR > QR?` (iii) `OR+OP > RP?`

Text Solution

AI Generated Solution

To solve the problem, we need to analyze the inequalities involving the lengths of segments formed by a point O inside triangle PQR. We will use the triangle inequality theorem, which states that in any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. ### Step-by-Step Solution: 1. **Consider the triangle PQR and point O inside it.** - We have triangle PQR with vertices P, Q, and R, and point O located inside this triangle. 2. **Evaluate the first inequality: OP + OQ > PQ.** ...
Promotional Banner

Topper's Solved these Questions

  • THE TRIANGLE AND ITS PROPERTIES

    NCERT|Exercise EXERCISE 6.5|8 Videos

  • THE TRIANGLE AND ITS PROPERTIES

    NCERT|Exercise EXERCISE 6.1|1 Videos

  • THE TRIANGLE AND ITS PROPERTIES

    NCERT|Exercise SOLVED EXAMPLES|6 Videos

  • SYMMETRY

    NCERT|Exercise EXERCISE 14.1|9 Videos

Similar Questions

Explore conceptually related problems

S in any point on side QR of a Delta PQR.Show that PQ + QR+RP gt 2PS.

In the givne figure, OA = OB and OP = OQ. Prove that (i) PX = QX, (ii) AX = BX.

S is any point on side QR of a DeltaPQR . Show that PQ+QR+RP gt 2PS .

O is a point in the interior of /_PQR such that OM perp QR and ON perp QP ,if /_PQR=60^(@), then find the value of /_NOM

In the given figure,OA=OB and OP=OQ. Prove that (i)PX=QX, (ii) AX=BX

Consider a circle with centre at C. Let OP, OQ denote respectively the tangents to the circle drawn from a point o outside the circle. Let R be a point on OP and S be a point on OQ such that OR xx SQ = OS xx RP . Which of the following statements is/are correct? 1. If X is the circle with centre at O and radius OR, and Y is the circle with centre at O and radius OS, then X = Y. 2. anglePOC +angleQCO=90^(@) Select the correct answer using the code given below.

In PQR,S is any point on the side QR. Show that PQ+QR+RP>2PS

In the figure, P is the point of contact. If OP=7.2,OQ=3.2, find OR and QR.

Angles Q and R of a DeltaPQR are 25^@ and 65^@. Write which of the following is true : (i) PQ^2+QR^2=RP^2 (ii) PQ^2+RP^2=QR^2 ( iii) RP^2+QR^2=PQ^2

If P be any point on the plane ln+my+nz=P and Q be a point on the line OP such that (OP)(OQ)=P^(2). The locus of point Q is