Advertisements
Advertisements
Question
In the given figure, ∠POQ = 100° and ∠PQR° = 30°, then find ∠RPO
Solution
∠PRQ = `1/2 ∠"POQ"` ...(Angles at the circumference)
= `1/2 xx 100^circ`
= 50°
∠OPQ + ∠OQP = 180° – 100° ...(Total angles of A is 180°)
= 80°
∴ ∠OPQ = `80/2`
= 40° ...(Since OP = OQ, radius of the circle)
∠RPQ = 180° − (30 + 50)°
= 100°
∴ ∠RPO = ∠RPQ – ∠OPQ
= 100° – 40°
= 60°
APPEARS IN
RELATED QUESTIONS
In the given figure, ABCD is a cyclic quadrilateral where diagonals intersect at P such that ∠DBC = 40° and ∠BAC = 60° find ∠CAD
In the given figure, ABCD is a cyclic quadrilateral where diagonals intersect at P such that ∠DBC = 40° and ∠BAC = 60° find ∠BCD
In the given figure, AB and CD are the parallel chords of a circle with centre O. Such that AB = 8 cm and CD = 6 cm. If OM ⊥ AB and OL ⊥ CD distance between LM is 7cm. Find the radius of the circle?
The arch of a bridge has dimensions as shown, where the arch measure 2m at its highest point and its width is 6m. What is the radius of the circle that contains the arch?
