Advertisements
Advertisements
प्रश्न
In the given figure P is a midpoint of chord AB of the circle O. prove that OP ^ AB.
Advertisements
उत्तर
Given:
In the figure, O is centre of the circle and ab is chord.
P is the mid-point of AB ⇒ AP = PB
To prove: OP ⊥ AB
Construction: Join OA and OB
Proof:
In ΔOAP and ΔOBP
OA = OB ....[radii of the same circle]
OP = OP ....[common]
AP = PB ....[given]
∴ By Side-Side-Side criterion of congruency,
ΔOAP ≅ ΔOBP
The corresponding parts of the congruent triangles are congruent.
∴ ∠OPA = ∠OPB
But ∠OPA + ∠OPB = 180° ....[linear pair]
∴ ∠OPA = ∠OPB = 90°
Hence OP ⊥ AB.
APPEARS IN
संबंधित प्रश्न
If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to `bar(EF)`
If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to `bar(DF)`
In the given figure, ∠P ≅ ∠R seg, PQ ≅ seg RQ. Prove that, ΔPQT ≅ ΔRQS.
In the pair of triangles in the following figure, parts bearing identical marks are congruent. State the test and the correspondence of vertices by the triangle in pairs is congruent.
The following figure has shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Prove that: (i) AM = AN (ii) ΔAMC ≅ ΔANB
State, whether the pairs of triangles given in the following figures are congruent or not:
Δ ABC in which AB = 2 cm, BC = 3.5 cm and ∠C = 80° and Δ DEF in which DE = 2 cm, DF = 3.5 cm and ∠D = 80°.
In the figure, AB = EF, BC = DE, AB and FE are perpendiculars on BE. Prove that ΔABD ≅ ΔFEC
Given that ∆ABC ≅ ∆DEF List all the corresponding congruent sides
If ∆PQR is congruent to ∆STU (see figure), then what is the length of TU?
The congruent figures super impose each other completely.
