Advertisements
Advertisements
प्रश्न
In the figure, given below, CP bisects angle ACB. Show that DP bisects angle ADB.
उत्तर
Given – In the figure, CP is the bisector of ∠ABC
To prove – DP is the bisector of ∠ADB
Proof – Since CP is the bisector of ∠ACB
∴ ∠ACP = ∠BCP
But ∠ACP = ∠ADP ...[Angle in the same segment of the circle]
And ∠BCP = ∠BDP
But ∠ACP = ∠BCP
∴ ∠ADP = ∠BDP
∴ DP is the bisector of ∠ADB
APPEARS IN
संबंधित प्रश्न
AB is a diameter of the circle APBR as shown in the figure. APQ and RBQ are straight lines. Find : ∠PRB
In a cyclic-trapezium, the non-parallel sides are equal and the diagonals are also equal. Prove it.
AB is a diameter of the circle APBR, as shown in the figure. APQ and RBQ are straight lines. Find : ∠BPR
A triangle ABC is inscribed in a circle. The bisectors of angles BAC, ABC and ACB meet the circumcircle of the triangle at points P, Q and R respectively. Prove that :
∠ACB = 2∠APR,
A triangle ABC is inscribed in a circle. The bisectors of angles BAC, ABC and ACB meet the circumcircle of the triangle at points P, Q and R respectively. Prove that :
`∠QPR = 90^circ - 1/2 ∠BAC`
In the given figure, ∠BAD = 65°, ∠ABD = 70° and ∠BDC = 45°. Find: ∠ ACB.
Hence, show that AC is a diameter.
If I is the incentre of triangle ABC and AI when produced meets the cicrumcircle of triangle ABC in points D . if ∠BAC = 66° and ∠ABC = 80°. Calculate : ∠IBC
If I is the incentre of triangle ABC and AI when produced meets the cicrumcircle of triangle ABC in points D. f ∠BAC = 66° and ∠ABC = 80°. Calculate : ∠BIC.
In the given Figure. P is any point on the chord BC of a circle such that AB = AP. Prove that CP = CQ.
In the figure, AB = AC = CD, ∠ADC = 38°. Calculate: (i) ∠ ABC, (ii) ∠ BEC.
