∠D = 80°
a. ∠C = 80° (∠D and ∠C are angled on a same arc So, both are equal)
b. ∠ABC = 90° (AC is diameter, Angle of a hemisphere is right)
c. ∠BAC = 180 – (80 + 90) = 180 – 170 = 100
d. ∠F= 180 – 80 = 100° (Opposite angles of a cyclic quadrilateral are equal)
Circles Memory Map
Angle in a semicircle is right:
The angle made by any arc of a circle on the alternate arc is half the angle made at the centre.
If ∠AOB = c°, then
∠APB = \(\frac{1}{2}c^\circ\).
All angles in an arc is equal:
If AB, CD are two chords, then
PA × PB = PC × PD
The area of the rectangle formed of parts into which a diameter of a circle is cut by a perpendicular chord is equal to the area of the square formed by half the chord.
PA × PB = PC2
