Advertisements
Advertisements
प्रश्न
In the given figure, PB is the bisector of ABC and ABC =ACB. Prove that:
a. BC x AP = PC x AB
b. AB:AC = BP: BC
उत्तर
a. Construction: Draw CE || BP and produce AB to E.
Proof: BP || EC
∠PBC = ∠BCE ...(Alternate angles)
∠ABP = ∠AEC ...(Corresponding angles)
Also, ∠ABP = ∠PBC
⇒ ∠BCE = ∠BEC
So, BE = BC
In ΔAEC,
⇒ `"AP"/"PC" = "AB"/"BE"`
⇒ BC x AP = PC x AB.
b. Note: It is not possible to prove this part due to inadequate data.
APPEARS IN
संबंधित प्रश्न
State, true or false:
All equiangular triangles are similar.
A line PQ is drawn parallel to the base BC of ∆ABC which meets sides AB and AC at points P and Q respectively. If AP = `1/3` PB; find the value of:
- `"Area of ΔABC"/"Area of ΔAPQ"`
- `"Area of ΔAPQ"/"Area of trapezium PBCQ"`
In ∆ABC, AP ⊥ BC, BQ ⊥ AC B– P–C, A–Q – C then prove that, ∆CPA ~ ∆CQB. If AP = 7, BQ = 8, BC = 12 then Find AC.
∆ABC and ∆DEF are equilateral triangles, A(∆ABC): A(∆DEF) = 1: 2. If AB = 4 then what is length of DE?
In Δ PQR, MN is drawn parallel to QR. If PM = x, MQ = (x-2), PN = (x+2) and NR = (x-1), find the value of x.
A model of a ship is made to a scale 1 : 300.
- The length of the model of the ship is 2 m. Calculate the length of the ship.
- The area of the deck of the ship is 180,000 m2. Calculate the area of the deck of the model.
- The volume of the model is 6.5 m3. Calculate the volume of the ship.
If ΔABC, D and E are points on AB and AC. Show that DE || BC for each of the following case or not:
AB = 10.8cm, BD = 4.5cm, AC = 4.8cm, and AE = 2.8cm
ΔABC is right angled at A. AD is drawn perpendicular to BC. If AB = 8cm and AC = 6cm, calculate BD.
A model of a ship is made to a scale of 1:500. Find: The area other deck o the ship, if the area of the deck of its model is m2
On a map drawn to a scale of 1:25000, a rectangular plot of land has sides 12cm x 16cm. Calculate: The diagonal distance of the plot in km
